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Benny Goodman

Benjamin David Goodman (May 30, 1909 – June 13, 1986) was an American clarinetist and bandleader, known as the "King of Swing".

From 1936 until the mid-1940s, Goodman led one of the most popular swing big bands in the United States. His concert at Carnegie Hall in New York City on January 16, 1938, is described by critic Bruce Eder as "the single most important jazz or popular music concert in history: jazz's 'coming out' party to the world of 'respectable' music."

Goodman's bands started the careers of many jazz musicians. During an era of racial segregation, he led one of the first integrated jazz groups, his trio and quartet. He continued performing up until the end of his life while also pursuing an interest in classical music.

Early years
Goodman was the ninth of twelve children born to poor Jewish emigrants from the Russian Empire. His father, David Goodman, came to the United States in 1892 from Warsaw in partitioned Poland and became a tailor. His mother, Dora Grisinsky, came from Kaunas. They met in Baltimore, Maryland, and moved to Chicago before Goodman's birth. With little income and a large family, they moved to the Maxwell Street neighborhood, an overcrowded slum near railroad yards and factories that was populated by German, Irish, Italian, Polish, Scandinavian, and Jewish immigrants.

Money was a constant problem. On Sundays, his father took the children to free band concerts in Douglass Park, which was the first time Goodman experienced live professional performances. To give his children some skills and an appreciation for music, his father enrolled ten-year-old Goodman and two of his brothers in music lessons, from 1919, at the Kehelah Jacob Synagogue. Benny also received two years of instruction from the classically trained clarinetist and Chicago Symphony member, Franz Schoepp. During the next year Goodman joined the boys club band at Hull House, where he received lessons from director James Sylvester. By joining the band, he was entitled to spend two weeks at a summer camp near Chicago. It was the only time he could get away from his bleak neighborhood. At 13, he got his first union card. He performed on Lake Michigan excursion boats, and in 1923 played at Guyon's Paradise, a local dance hall.

In the summer of 1923, he met cornetist and composer Bix Beiderbecke. He attended the Lewis Institute (Illinois Institute of Technology) in 1924 as a high-school sophomore and played clarinet in a dance hall band. When he was 17, his father was killed by a passing car after stepping off a streetcar, which Goodman called "the saddest thing that ever happened in our family".

Early career
His early influences were New Orleans jazz clarinetists who worked in Chicago, such as Jimmie Noone, Johnny Dodds, and Leon Roppolo. He learned quickly, becoming a strong player at an early age, and was soon playing in bands. He made his professional debut in 1921 at the Central Park Theater on the West Side of Chicago. He entered Harrison Technical High School in Chicago in 1922. At fourteen he became a member of the musicians' union and worked in a band featuring Bix Beiderbecke. Two years later he joined the Ben Pollack Orchestra and made his first recordings, in 1926.

From sideman to bandleader
Goodman moved to New York City and became a session musician for radio, Broadway musicals, and in studios. In addition to clarinet, he sometimes played alto saxophone and baritone saxophone. His first recording pressed to disc (Victor 20394) occurred on December 9, 1926, in Chicago. The session resulted in the song "When I First Met Mary", which also included Glenn Miller, Harry Goodman, and Ben Pollack. In a Victor recording session on March 21, 1928, he played alongside Miller, Tommy Dorsey, and Joe Venuti in the All-Star Orchestra directed by Nathaniel Shilkret. He played with the bands of Red Nichols, Ben Selvin, Ted Lewis, and Isham Jones and recorded for Brunswick under the name Benny Goodman's Boys, a band that featured Glenn Miller. In 1928, Goodman and Miller wrote "Room 1411", Miller's first known composition, which was released as a Brunswick 78.

He reached the charts for the first time in January 1931 with "He's Not Worth Your Tears", featuring a vocal by Scrappy Lambert for Melotone. After signing with Columbia in 1934, he had top ten hits with "Ain't Cha Glad?" and "I Ain't Lazy, I'm Just Dreamin'" sung by Jack Teagarden, "Ol' Pappy" sung by Mildred Bailey, and "Riffin' the Scotch" sung by Billie Holiday. An invitation to play at the Billy Rose Music Hall led to his creation of an orchestra for the four-month engagement. The orchestra recorded "Moonglow", which became a number one hit and was followed by the Top Ten hits "Take My Word" and "Bugle Call Rag".

NBC hired Goodman for the radio program Let's Dance. John Hammond asked Fletcher Henderson if he wanted to write arrangements for Goodman, and Henderson agreed. During the Depression, Henderson disbanded his orchestra because he was in debt. Goodman hired Henderson's band members to teach his musicians how to play the music.

Goodman's band was one of three to perform on Let's Dance, playing arrangements by Henderson along with hits such as "Get Happy" and "Limehouse Blues" by Spud Murphy.

Goodman's portion of the program was broadcast too late at night to attract a large audience on the east coast. He and his band remained on Let's Dance until May of that year when a strike by employees of the series' sponsor, Nabisco, forced the cancellation of the radio show. An engagement was booked at Manhattan's Roosevelt Grill filling in for Guy Lombardo, but the audience expected "sweet" music and Goodman's band was unsuccessful.

Goodman spent six months performing on Let's Dance, and during that time he recorded six more Top Ten hits for Columbia.

Catalyst for the swing era

On July 31, 1935, "King Porter Stomp" was released with "Sometimes I'm Happy" on the B-side, both arranged by Henderson and recorded on July 1. In Pittsburgh at the Stanley Theater some members of the audience danced in the aisles. But these arrangements had little impact on the tour until August 19 at McFadden's Ballroom in Oakland, California. Goodman and his band, which included Bunny Berigan, drummer Gene Krupa, and singer Helen Ward were met by a large crowd of young dancers who cheered the music they had heard on Let's Dance. Herb Caen wrote, "from the first note, the place was in an uproar." One night later, at Pismo Beach, the show was a flop, and the band thought the overwhelming reception in Oakland had been a fluke.

The next night, August 21, 1935, at the Palomar Ballroom in Los Angeles, Goodman and his band began a three-week engagement. On top of the Let's Dance airplay, Al Jarvis had been playing Goodman's records on KFWB radio. Goodman started the evening with stock arrangements, but after an indifferent response, he began the second set with arrangements by Fletcher Henderson and Spud Murphy. According to Willard Alexander, the band's booking agent, Krupa said, "If we're gonna die, Benny, let's die playing our own thing." The crowd broke into cheers and applause. News reports spread word of the exciting music and enthusiastic dancing. The Palomar engagement was such a marked success that it is often described as the beginning of the swing era. According to Donald Clarke, "It is clear in retrospect that the Swing Era had been waiting to happen, but it was Goodman and his band that touched it off."

The reception of American swing was less enthusiastic in Europe. British author J. C. Squire filed a complaint with BBC Radio to demand it stop playing Goodman's music, which he called "an awful series of jungle noises which can hearten no man." Germany's Nazi party barred jazz from the radio, claiming it was part of a Jewish conspiracy to destroy the culture. Italy's fascist government banned the broadcast of any music composed or played by Jews which they said threatened "the flower of our race, the youth."

In November 1935, Goodman accepted an invitation to play in Chicago at the Joseph Urban Room at the Congress Hotel. His stay there was extended to six months, and his popularity was cemented by nationwide radio broadcasts over NBC affiliate stations. While in Chicago, the band recorded "If I Could Be with You (One Hour Tonight)", "Stompin' at the Savoy", and "Goody Goody". Goodman also played three concerts produced by Chicago socialite and jazz aficionado Helen Oakley. These "Rhythm Club" concerts at the Congress Hotel included sets in which Goodman and Krupa sat in with Fletcher Henderson's band, perhaps the first racially integrated big band appearing before a paying audience in the United States. Goodman and Krupa played in a trio with Teddy Wilson on piano. Both combinations were well received, and Wilson remained.

In his 1935–1936 radio broadcasts from Chicago, Goodman was introduced as the "Rajah of Rhythm". Slingerland Drum Company had been calling Krupa the "King of Swing" as part of a sales campaign, but shortly after Goodman and his crew left Chicago in May 1936 to spend the summer filming The Big Broadcast of 1937 in Hollywood, the title "King of Swing" was applied to Goodman by the media.

At the end of June 1936, Goodman went to Hollywood, where, on June 30, 1936, his band began CBS's Camel Caravan, its third and (according to Connor and Hicks) its greatest sponsored radio show, co-starring Goodman and his former boss Nathaniel Shilkret. By spring 1936, Fletcher Henderson was writing arrangements for Goodman's band.

Carnegie Hall concert
In late 1937, Goodman's publicist Wynn Nathanson suggested that Goodman and his band play Carnegie Hall in New York City. The sold-out concert was held on the evening of January 16, 1938. It is regarded as one of the most significant concerts in jazz history. After years of work by musicians from all over the country, jazz had finally been accepted by mainstream audiences—according to Stan Ayeroff, "the concert helped jazz evolve from being strictly dance music to music worthy of a discerning listening audience. It was the start of jazz being recognized as an art form on a par with classical music."

Recordings of the concert were made, but even by the technology of the day the equipment used was not of the finest quality. These recordings were made on acetate, and aluminum studio masters were cut. The idea of recording the concert came from Albert Marx, a friend of Goodman's, for the purposes of a gift for his wife Helen Ward, as well as gifting a second set to Goodman. Sometime in or before 1950, Goodman recovered the acetates from his sister-in-law's closet, who had informed him about them, and took them to the audio engineer William Savory. The pair took them to Columbia, with Goodman realising the recordings could be used as leverage to make a recording contract with Columbia (having been eager to end his contract with Capitol). A selection was then released as an LP entitled The Famous 1938 Carnegie Hall Jazz Concert.

Charlie Christian

In 1939, pianist and arranger Mary Lou Williams suggested to John Hammond, who was responsible for finding new talent for Goodman, that he see guitarist Charlie Christian. Hammond had seen Christian perform in Oklahoma City on July 10, 1939, and recommended him to Goodman, but Goodman was uninterested in electric guitar and was put off by Christian's taste in gaudy clothing. Unbeknownst to Goodman, at a August 16 concert at the Victor Hugo Restaurant in Beverly Hills, Hammond inserted Christian onto the stage. Goodman started playing "Rose Room" on the assumption that Christian didn't know it, but his performance impressed the audience immensely. According to Hammond, "before long the crowd was screaming with amazement. 'Rose Room' continued for more than three quarters of an hour and Goodman received an ovation unlike any even he had before. No one present will ever forget it, least of all Benny."

Christian was a member of the Benny Goodman Sextet from 1939 to 1941, and during these two years he turned the electric guitar into a popular jazz instrument.

Decline of swing
Goodman continued his success throughout the late 1930s with his big band, his trio and quartet, and the sextet formed in August 1939, the same month Goodman returned to Columbia Records after four years with RCA Victor. At Columbia, John Hammond, his future brother-in-law, produced most of his sessions. By the mid-1940s, however, big bands had lost much of their popularity. In 1941, ASCAP had a licensing war with music publishers. From 1942 to 1944, and again in 1948, the musicians' union went on strike against the major record labels in the United States, and singers acquired the popularity that the big bands had once enjoyed. During the 1942–44 strike, the War Department approached the union and requested the production of V-Discs, a set of records containing new recordings for soldiers, thereby boosting the rise of new artists. Also, by the late 1940s, swing was no longer the dominant style of jazz musicians.

Exploring bebop
By the 1940s, some jazz musicians were borrowing from classical music, while others, such as Charlie Parker, were broadening the rhythmic, harmonic, and melodic vocabulary of swing to create bebop (or bop). The bebop recordings Goodman made for Capitol were praised by critics. For his bebop band he hired Buddy Greco, Zoot Sims, and Wardell Gray. He consulted his friend Mary Lou Williams for advice on how to approach the music of Dizzy Gillespie and Charlie Parker. Pianist Mel Powell was also an adviser in 1945. Goodman enjoyed bebop. When he heard Thelonious Monk, he said, "I like it, I like that very much. I like the piece and I like the way he played it ... I think he's got a sense of humor and he's got some good things there." He also admired Swedish clarinetist Stan Hasselgård. But after playing with a bebop band for over a year, he returned to his swing band because he concluded that was what he knew best. In 1953, he said, "Maybe bop has done more to set music back for years than anything ... Basically it's all wrong. It's not even knowing the scales ... Bop was mostly publicity and people figuring angles."

Classical repertoire
In 1949 he studied with clarinetist Reginald Kell, requiring a change in technique: "instead of holding the mouthpiece between his front teeth and lower lip, as he had done since he first took a clarinet in hand 30 years earlier, Goodman learned to adjust his embouchure to the use of both lips and even to use new fingering techniques. He had his old finger calluses removed and started to learn how to play his clarinet again—almost from scratch."

Goodman commissioned compositions for clarinet and chamber ensembles or orchestra that have become standard pieces of classical repertoire. He premiered works by composers, such as Contrasts by Béla Bartók; Clarinet Concerto No. 2, Op. 115 by Malcolm Arnold; Derivations for Clarinet and Band by Morton Gould; Sonata for Clarinet and Piano by Francis Poulenc, and Clarinet Concerto by Aaron Copland. Prelude, Fugue, and Riffs by Leonard Bernstein was commissioned for Woody Herman's big band, but it was premiered by Goodman. Herman was the dedicatee (1945) and first performer (1946) of Igor Stravinsky's Ebony Concerto, but many years later Stravinsky made another recording with Goodman as the soloist.

He made a recording of Mozart's Clarinet Quintet in July 1956 with the Boston Symphony String Quartet at the Berkshire Festival; on the same occasion he recorded Mozart's Clarinet Concerto in A major, K. 622, with the Boston Symphony Orchestra conducted by Charles Munch. He also recorded the clarinet concertos of Weber

After forays outside swing, Goodman started a new band in 1953. According to Donald Clarke, this was not a happy time for Goodman. He reunited the band to tour with Louis Armstrong. But he insulted Armstrong and "was appalled at the vaudeville aspects of Louis's act...a contradiction of everything Goodman stood for". Armstrong left Goodman hanging during a joint performance where Goodman called Armstrong back onstage to wrap up the show. Armstrong refused to perform alongside Goodman, which led essentially to the end of their friendship.

Goodman's band appeared as a specialty act in the films The Big Broadcast of 1937; Hollywood Hotel (1938); Syncopation (1942); The Powers Girl (1942); Stage Door Canteen (1943); The Gang's All Here (1943); Sweet and Low-Down (1944), Goodman's only starring feature; Make Mine Music (1946) and A Song Is Born (1948).

Later years
He continued to play on records and in small groups. In the early 1970s he collaborated with George Benson after the two met taping a PBS tribute to John Hammond, recreating some of Goodman's duets with Charlie Christian. Benson appeared on Goodman's album Seven Come Eleven. Goodman continued to play swing, but he practiced and performed classical pieces and commissioned them for clarinet. In 1960 he performed Mozart's Clarinet Concerto with conductor Alfredo Antonini at the Lewisohn Stadium in New York City. Despite health problems, he continued to perform, his last concert being six days before his death. Goodman died on June 13, 1986, from a heart attack while taking a nap at his apartment in Manhattan House.

Personal life
One of Goodman's closest friends was Columbia producer John Hammond, who influenced Goodman's move from Victor to Columbia. Goodman married Hammond's sister, Alice Frances Hammond Duckworth (1905–1978), on March 20, 1942. They had two daughters and raised Alice's three daughters from her first marriage to British politician Arthur Duckworth. Goodman's daughter Rachel became a classical pianist. She sometimes performed in concert with him, beginning when she was sixteen.

Goodman and Hammond had disagreements from the 1930s onwards. For the 1939 Spirituals to Swing concert Hammond had placed Charlie Christian into the Kansas City Six to play before Goodman's band, which had angered Goodman. They disagreed over the band's music until Goodman refused to listen to Hammond. Their arguments escalated, and in 1941 Hammond left Columbia. Goodman appeared on a 1975 PBS tribute to Hammond but remained at a distance. In the 1980s, after the death of Alice Goodman, Hammond and Goodman reconciled. On June 25, 1985, Goodman appeared at Avery Fisher Hall in New York City for "A Tribute to John Hammond".

Goodman was regarded by some as a demanding taskmaster, by others as an arrogant and eccentric martinet. Many musicians spoke of "The Ray", the glare that Goodman directed at a musician who failed to perform to his standards. After guitarist Allan Reuss incurred Goodman's displeasure, Goodman relegated him to the rear of the bandstand where his contribution would be drowned out by the other musicians. Vocalists Anita O'Day and Helen Forrest spoke bitterly of their experiences singing with Goodman: "The twenty or so months I spent with Benny felt like twenty years," said Forrest. "When I look back, they seem like a life sentence." He was generous and funded several college educations, though always secretly. When a friend asked him why, he said, "Well, if they knew about it, everyone would come to me with their hand out."

Goodman helped racial integration in America. In the early 1930s, black and white musicians could not play together in most clubs and concerts. In the Southern states, racial segregation was enforced by Jim Crow laws. Goodman hired Teddy Wilson for his trio and added vibraphonist Lionel Hampton for his quartet. In 1939 he hired guitarist Charlie Christian. This integration in music happened ten years before Jackie Robinson broke Major League Baseball's six-decade-long color line. According to Jazz (Episode 5) by Ken Burns, Lionel Hampton states that when someone asked Goodman why he "played with that nigger" (referring to Teddy Wilson), Goodman replied, "If you say that again to me, I'll take a clarinet and bust you across your head with it".

In 1962, the Benny Goodman Orchestra toured the Soviet Union as part of a cultural exchange program between the two nations after the Cuban Missile Crisis and the end of that phase of the Cold War; both visits were part of efforts to normalize relations between the United States and the USSR. Members of the band included Jimmy Knepper, Jerry Dodgion, and Turk Van Lake (Vanig Hovsepian). Bassist Bill Crow published a very jaundiced view of the tour and Goodman's conduct during it under the title "To Russia Without Love".

Awards and honors

Goodman was honored with the Grammy Lifetime Achievement Award.

After winning polls as best jazz clarinetist, Goodman was inducted into the Down Beat Jazz Hall of Fame in 1957.

He was a member of the radio division of the National Association of Broadcasters Hall of Fame.

His papers were donated to Yale University after his death. He received honorary doctorates from Union College, the University of Illinois, Southern Illinois University Edwardsville, Bard College, Brandeis University, Columbia University, Harvard University, and Yale University.

Partial discography

 * Swinging 34 Vols. 1 & 2 (Melodeon, 1934)
 * Original Benny Goodman Trio and Quartet Sessions, Vol. 1: After You've Gone (Bluebird, 1935)
 * Stomping at the Savoy (Bluebird, 1935)
 * Air Play (Doctor Jazz, 1936)
 * Sing, Sing, Sing (With a Swing) (Columbia, 1937)
 * Roll 'Em, Vol. 1 (Columbia, 1937)
 * Roll 'Em, Vol. 2 (Columbia, 1937)
 * Don't Be That Way (Columbia 1938)
 * From Spirituals to Swing (Vanguard, 1938)
 * The Famous 1938 Carnegie Hall Jazz Concert Vols. 1–3 (Columbia, 1938)
 * Mozart Clarinet Quintet, with the Budapest String Quartet (RCA Victor, 1938)
 * Eddie Sauter Arrangements (Columbia, 1940)
 * Swing into Spring (Columbia, 1941)
 * Benny Goodman Sextet (Columbia, 1944)
 * Undercurrent Blues (Capitol, 1947)
 * Swedish Pastry (Dragon, 1948)
 * Session for Six (Capitol, 1950)
 * The Benny Goodman Trio Plays (Columbia, 1951)
 * Goodman & Teagarden (Jazz Panorama, 1951)
 * Easy Does It (Capitol, 1952)
 * Benny at the Ballroom (Columbia, 1955)
 * BG in Hi-Fi (Capitol, 1955)
 * Mozart Clarinet Concerto with the Boston Symphony Orchestra (1956)
 * Mostly Sextets (Capitol, 1956)
 * The Great Benny Goodman (Columbia, 1956)
 * Peggy Lee Sings with Benny Goodman (Harmony, 1957)
 * Benny Rides Again (1958)
 * Benny Goodman Plays World Favorites in High Fidelity (1958)
 * Benny in Brussels Vols. 1 and 2 (Columbia, 1958)
 * In Stockholm 1959 (Phontastic, 1959)
 * The Benny Goodman Treasure Chest (MGM, 1959)
 * The Hits of Benny Goodman (Capital Records, 1961)
 * Benny Goodman in Moscow (RCA Victor, 1962)
 * Weber Clarinet Concertos Nos. 1 and 2 with the Chicago Symphony (RCA, 1968)
 * London Date (Phillips, 1969)
 * Benny Goodman Today (London, 1970)
 * This Is Benny Goodman (RCA Victor, 1971)
 * Benny Goodman – A Legendary Performer (RCA, 1977)
 * Benny Goodman Live at Carnegie Hall: 40th Anniversary Concert (1978)
 * Benny Goodman – Live in Hamburg 1981 (Stockfisch, 2019)

Posthumous

 * Sing, Sing, Sing (Bluebird, 1987)
 * The Benny Goodman Sextet Featuring Charlie Christian: 1939–1941
 * 16 Most Requested Songs (Columbia/Legacy, 1993)
 * 1935–1938 (1998)
 * Carnegie Hall Jazz Concert '38 (1998)
 * Bill Dodge All-star Recording (1999)
 * 1941–1955 His Orchestra and His (1999)
 * Live at Carnegie Hall (1999)
 * Carnegie Hall: The Complete Concert (2006)
 * The Yale University Music Library, Vol. 2: Live at Basin Street (Musical Heritage Society, 1988)
 * The Complete RCA Victor Small Group Recordings (RCA Victor, 1997)
 * Lausanne 1950 (Swiss Radio Days Theatre De Beaulieu, May 13, 1950 TCB 2005)

title: Benny Goodman


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Talk:Completeness

completeness
Would it not be a good idea to have Completeness as a dictionary style definition, leading off to: etc? -- Anon
 * Completeness (metric spaces)
 * Completeness (measures)
 * Completeness (logic)

Yes, I agree that this would make a good disambiguation page. However at this point, it's not really necessary; the metric (or uniform) space concept is the only one that has had enough written about it to form an entire article. Thus, I have created Complete_space, which currently redirects here, in anticipation of this, and we can link to that page instead of this if we wish. However, I don't think that it's necessary to move the contents of this article over there, or to move links to this article over there, until we reach the point that there is either: Then we can do the transition; otherwise, the move may be harmless but is largely a waste of time. IMO. -- Toby Bartels, Monday, June 10, 2002
 * a great deal written about completeness in some other article (such as the article on lattices) that justifies branching it off to a new article, or
 * a great deal written about one of the other sorts of completeness in this article that justifies splitting this into two articles.

The main content of this page may need to be moved to complete_metric, or something similar, but it would not be sensible to do this until Pages_that_link_here is fixed. -- Anon

If and when we move it, it should be to Complete_space, since we'll want to discuss other notions of complete spaces (complete uniform spaces, maybe even complete Cauchy spaces) under the heading Generalisations. — Toby Bartels, Sunday, July 14, 2002

Given that Complete measure is a separate article, I'm doing the move now. -- Toby 23:40 Feb 20, 2003 (UTC)

- I removed
 * If V is separable, it follows that any vector in V can be written as a (possibly infinite) linear combination of vectors from S.

Linear combinations are by definition finite, so we would have to say a bit more to make this statement precise. Even then, I'm not sure that it is true in general (it surely works in Hilbert spaces though). AxelBoldt 18:12 29 May 2003 (UTC)

Our article now discusses infinite linear combinations. -- Toby Bartels 09:43, 26 Aug 2003 (UTC)

I agree that if non-mathematical usages are to be included, that should be a separate page. But perhaps in that case, this page should be moved to "Completeness (mathematics)", or, if that's a bit too narrow, "Completeness (mathematical sciences)". Michael Hardy 01:57, 15 Sep 2003 (UTC)

Michael, you said "Not all ordered fields are metric spaces; this is not merely a special case of the metric space case." You are correct, of course, but the concept of a Cauchy sequence is still meaningful in nonmetric ordered fields. Every ordered field has a unique subfield isomorphic to the rational numbers, so a Cauchy sequence is just one in which the difference between every pair of elements for some point onward corresponds to a rational number less than the given real number.

This won't work, (I'm thinking this out, even as I type.), since the differences between the elements in a Cauchy sequence need not be rational. It would work if instead of the subfield isomorphic to the rationals, we used the largest subfield isomorphic to a subfield of the reals. But it's not clear to me that such a subfield must always exist, or that it's always unique.

Please revert if what I wrote was Patent nonsense. But there is a connection between the two definitions, which should be made clear somehow. -- Daran 06:14, 15 Sep 2003 (UTC)

Proof theory subsection
The subection currently reads:

 * In proof theory and related fields of mathematical logic, a formal calculus is said to be complete with respect to a certain logic (i.e. with respect to its semantics), if every statement P that follows semantically from a set of premises G can be derived syntactically from these premisses within the calculus. Formally, implies  . Especially, all tautologies of the logic can be proven. Even when working with classical logic, this is not equivalent to the notion of completeness introduced above (both a statement and its negation might not be tautologies with respect to the logic). The reverse implication is called soundness.

Two things: (i)This notion is not really native to proof theory, although it originated there, but is rather one of the fundamental ideas of model theory. (ii)Completeness is not restricted to logic; it makes perfect sense to talk about completeness wrt to any first-order theory. Charles Stewart 11:52, 29 Sep 2004 (UTC)

tautologies
Lambiam, the goal here is to account for the properties of the logical system without regard to meaning or semantics. This is the primary, fundamental, canonical definition of completeness. What you say is true (of semantic completeness), however, that formulation of completeness is a little further down the road from syntactic completeness, so to speak.

Strictly speaking, it is not necessarily true, as you have worded it, that: "A logical system has "completeness" when all true sentences (given the semantics of the logic) are theorems, whereas a formal system has "soundness" when all theorems are true sentences." ...because we can talk about the completeness of logical systems without regard to semantics (the idea that certain sentences are true or false) at all. Pontiff Greg Bard (talk) 12:30, 27 January 2008 (UTC)

 * How would you determine whether (for example) the formula [a*](p → [a]p) → (p → [a*]p) is a tautology? The definition given in our article Tautology applies only to a rather narrow set of simple logics. --Lambiam 17:42, 27 January 2008 (UTC)

 * "Tautology" is the more general term here. All "true sentences" are tautologies, however not all tautologies are "true sentences." That's a good quiz question. It looks like one of the principles of modal logic. That's a quantifier, not some kind of Kleene star right? I'm going to get back to you at some point for your example. It is the formation of the symbols, "→", "p", etc, that determine whether it is a tautology or not, not any interpretation of, for instance, p being true. So for instance, if your example is a tautology, then it is a token or the type of tautology that is:

 * [a*](x → [a]x) → (x → [a*]x)

 * I haven't taken a close look at tautology yet. The uninterpreted tautology may need elucidation. Be well, Pontiff Greg Bard (talk) 00:14, 28 January 2008 (UTC)

 * It is a theorem that is an easy consequence of axiom A6 of dynamic logic. The [...] is sort of a modal operator, and the argument like a* is from a Kleene algebra, where the * is the Kleene star.
 * I don't understand your sentence "it is a token or the type of tautology that is ...".
 * Can you give a source for a definition of "tautology" in the sense you understand it, and an example of a tautology that is not a true sentence? Or do you just mean that "A = A" is not true because "A" is a variable?
 * --Lambiam —Preceding comment was added at 06:32, 28 January 2008 (UTC)

 * If that is a kleene star, I really don't know much about its properties. I cannot vouch for the accuracy of the above statement on those grounds. However, also, Please forgive my error. It's supposed to be:

 * "...it is a token of the type OF tautology that is..."

 * The things we are talking about are abstract objects. They are "types" of things. They do not exist in any particular place or time. We only see tokens of them. The ink on the paper, or the actual chalk on the board may also be a "tautology." However, it is the properties of the abstract version that we are talking about here.

 * I think your statement "...do you just mean that "A = A" is not true because "A" is a variable?" is another way of looking at the idea I am trying to explain. These are syntactic qualities. I will look further into these matters and try to get a good example. In lieu of that good example, I will provide the principle that makes me know that it exists: A formal system is complete with respect to the property of tautologousness iff every sentence that is a tautology is a theorem. (This is from the second definition in that bullet list). There do exist systems that are not complete with respect to the property of tautologousness. I think the FS system I described at Talk:Theorem qualifies, although I think there are better examples out there. Be well, Pontiff Greg Bard (talk) 07:54, 28 January 2008 (UTC)

 * If by FS you mean the system with theorems of the form †∗m+1†∗n then I must confess I haven't the foggiest idea what it means for a string of daggers and asterisks to be a tautology, and so your statement that this system may qualify as not being complete in your sense of the term carries no content for me. I am still waiting for (1) a source for a definition of "tautology" in the sense you understand it, and (2) an example of a tautology that is not a true sentence. --Lambiam 12:56, 28 January 2008 (UTC)

 * I guess my next question is what does "carries no content for me" mean? Does it mean a) you just would like more clarification, b) you are indifferent to the clarifications I have made, and will be going ahead with your version, or c) you understand it as trivial, or d) something else? The other question I have is how long are you willing to wait for (1) and (2)? I think the fact that this type of formula can be a non-tautologous theorem should really inform and enhance your notion of tautology. That's is what I would like for the readers. Pontiff Greg Bard (talk) 15:10, 28 January 2008 (UTC) Pontiff Greg Bard (talk) 15:10, 28 January 2008 (UTC)

 * It carries no content for me in the sense that I am unable to assign meaning to that string of words, presumably in the same way you can't extract meaningful content from a statement that "the rights of cloud precede mutation". In technical terms, the utterance is inoperative as a truthbearer.
 * How long do you expect me to wait? Given the meaning of completeness that I know and see in the literature, the article is wrong, but you reverted my fix with arguments that I don't comprehend. --Lambiam 18:35, 28 January 2008 (UTC)

 * Well Lambiam, let me first say that I appreciate your care and attention to these matters. Our discussion has been a pleasure on my part. As you may know, I am not always very diplomatic, so please forgive my forthright conjecture. I can tell you have studied this subject well. It is clear that you understand what you say you understand, and you are forthright on these points where you are not 100% clear. However, I think what you do understand is not permitting this new understanding. This actually is the more fundamental understanding, not trivial at all, perhaps you have been mathematically prejudiced.

 * The formal language with stars and daggers can form theorems, as described at Talk:Theorem. A good way to understand these things is like moving boxes. If you have a map (or a checkerboard or whatever), and some rules you can move boxes to some places and not others. The places the rules allow you to move a box is a theorem. Perhaps more appropriate to the analogy, the box is a theorem in some places not others. So this is a totally new understanding of theorem. It doesn't involve "true" or "proved." Calling a box a theorem will certainly seem strange to a mathematician, however this is what is going on behind the scenes. It is not appropriate to say "Well but it isn't REALLY a theorem." That would be missing the point entirely. It is exactly this that is the essence of theorem. This is what it is like to talk about syntax without semantics. The same analogy goes for tautologies, although I found theorem easier to explain.

 * I hope at some point this results in an "aha moment" rather than impatience with myself. I am only a cab driver, so I am learning a lot more from others than I am contributing. However, these appear to be concepts that mathematicians in general do not care about or, pay attention to, and that is fine. However, it should not be looked upon as foreign or hostile at all. Please look at it as filling in the philosophical perspective. It seems to me that in philosophy classes we are told that mathematicians study this area too, but the mathematicians are not told that we study this area too (or they are told and promptly shrug them off as pretenders --silly).

 * There are no deadlines on wp, so I don't really have a good answer. The next time I get to the university library perhaps? It seems that the article is tagged for no sources so it really boils down to what we agree on until there are. I guess I could rightly ask you when you will come up with sources for your language too, however I'm not that way. I am quite sure there are sources that support both formulations, however yours belongs a little later in the article because of it involves an interpretation of the pure thing we are talking about. There is no good statement about semantic completeness in the article, so I think your formulation (which I reverted) belongs in under that. However, I do not have a good canonical account, so I didn't put it in there because I could do it justice just yet. Be well, Pontiff Greg Bard (talk) 00:14, 29 January 2008 (UTC)

 * I have no problem with accepting †∗∗†∗ as a theorem of some logical system. What I don't get is what it means to state that it is, or is not, a tautology.
 * In the meantime, let me give some references to definitions of soundness and completeness in various texts:
 * Michael O'Donnell. In Handbook of Logic in Artificial Intelligence and Logic Programming pp. 40–41.
 * Greg Restall. An Introduction to Substructural Logics pp. 181–182.
 * Torkel Franzen. Inexhaustibility: A Non-exhaustive Treatment pp. 107–108.
 * Robert L. Causey. Logic, Sets, and Recursion p. 72
 * The last of these is particularly interesting because the author uses the terminology "tautological consequence" but makes it explicit in the notation that this corresponds to the semantic notion of entailment, bolstering my contention that being a tautology is a semantic property. --Lambiam 08:43, 29 January 2008 (UTC)

 * A semantic tautology is a wff of truth-functional propositional logic whose truth table column contains nothing but T's when these are interpreted as the truth-value Truth. A syntactic tautology is a wff of truth-functional logic whose truth table column contains nothing but T's when these T's are uninterpreted tokens rather than, say, truth-values. The rules for generating the truth table column tell us to use one of these uninterpreted T's in exactly those cases where semantic considerations would have led us to use the truth-value Truth. This can be found at this Glossary of first order logic. The syntactic qualities should be covered first, and then the many and varied semantic aspects should supplement. Like I implied earlier, we are both right. Be well, Pontiff Greg Bard (talk) 20:22, 29 January 2008 (UTC)
 * Thank you for your recent contribution to effective method. I learned something new about it. Pontiff Greg Bard (talk) 20:39, 29 January 2008 (UTC)

(exdent) May I say that I find the distinction between semantic tautology and syntactic tautology inane? I could likewise define semantic equality and syntactic equality. Take an equation such as 5 + 9 = 2 × 7. Evaluate both sides, using tables of addition and multiplication. If this results in equal numbers, interpreting the entries in the tables as numbers, it is semantic equality. If the same exercise leads to equal strings, interpreting the entries in the tables as strings of digits, it is syntactic equality. Well, the two notions will never give an observable difference, not for these equalities and not for tautologies. The statement that the two always give rise to the same verdict is itself a tautology. We may as well distinguish between normal tautologies, en upside-down tautologies, where the latter are obtained by Australians, New Zealanders, and some yoga practioning logicians. It is somewhat amazing that the author does not distinguish between semantic soundness and syntactic soundness. Whether semantic or syntactic, it doesn't say anything about how to defined the notion for other logical systems than propositional logic. It is hard to imagine a non-semantical method to evaluate quantifications. --Lambiam 23:39, 29 January 2008 (UTC)

 * You understand that this kind of supports my whole "mathematical prejudice" theory do you not? You are going to interpret a number as a number, huh? Yeah that seems pretty silly. Only that is not what is going on here. It's not a number until it is interpreted as such, until then it is just a symbol. We are able to move symbols around on paper according to rules, and get other symbols that happen to preserve deductive qualities. This is the level of analysis we seek, because we want to make sure we have a legitimate deductive system, with no presuppositions (as you have made about the so-called "equal numbers" you speak of.) We can see today that Euclid fudged somewhat on the rigor of some of his proofs. I'm sure he thought it was okay at the time. Mathematics is orders of magnitude more complex today, so BE CAREFUL! ...and be well. Pontiff Greg Bard (talk) 15:04, 30 January 2008 (UTC)

 * I know that I really understand the meaning, but how do I know you are capable of real understanding of the concept of Truth and not just mechanically scanning for a column of uninterpreted "T" symbols? Even if you say you understand, for all I know, your "semantic" interpretation is nothing but pushing symbols around in a neural network. We are really getting into the other minds problem here. The distinction between the two notions of tautology is, however, really mainly silly because they necessarily always coincide. Would you ask someone who states "¬(A ∧ ¬A) is a tautology" to clarify whether they mean a semantic tautology or a syntactic tautology? --Lambiam 19:03, 30 January 2008 (UTC)

 * Congratulations, you are now a philosopher. I will look into your answerable question at some point! Be well, Pontiff Greg Bard (talk) 22:20, 30 January 2008 (UTC)

Making it saner
This page is crazy! It is the Ersatz for the deceptively short disambiguation page for "Completion", mixes completely unrelated subjects, such as auditing, autocompletion, and complete metric spaces, etc, etc. I was originally looking for a link to completion of rings in commutative algebra, in order to add it to one of the articles I was editing, and was nary certain it's not even mentioned. Tells you how easy it is to find stuff here! I strongly propose at least to move out the mathematical uses of "complete" and "completion" that have nothing to do with logic, finances, or philosophy into "Complete (mathematics)", as was proposed by Michael Hardy already 5 years ago. Arcfrk (talk) 08:16, 1 March 2008 (UTC)

 * This page should be turned into a standard disambiguation page, conforming to the rules of MOS:DAB. Furthermore, it should be merged with Completion (disambiguation), so that the page starts with s.t. like "Complete, completeness and completion can refer to:". Finally, I think the page Completion should be moved to Well completion; it is zany that the latter use of the term, which is not even mentioned in any dictionary I have access to and does not occur (except for the Wikipedia article) in the first 100 Google hits for "completion", should have primacy. Funny fact: Quadratic reciprocity currently links to Completion.
 * Whether the above can garner consensus or not, there is no impediment to starting a page Complete (mathematics) now. However, I consider mathematical logic as much a field of mathematics as category theory, graph theory, analysis, and algebra, and I strongly disagree with the idea of banning the meanings in mathematical logic from such a page. --Lambiam 08:56, 7 March 2008 (UTC)

 * I agree with the disambiguation proposal to merge. I would prefer it if we merely designated this article space as the disambiguation page without the "(disambiguation)" in the title. I'm not so keen on separating out the "(mathematics)" however. I find that whole (very strong apparently) tendency towards disintegration not helpful at all. Pontiff Greg Bard (talk) 18:20, 19 March 2008 (UTC)

 * This discussion is very old, but the well completion page is now a redirect to its more common meaning, related to drilling wells - which has nothing to do with the concept of mathematical completeness. Every page that links to that article uses it in that context.  This talk-page is the only place that links to "well completion" to refer to the mathematical sense.  Nimur (talk) 14:35, 4 May 2010 (UTC)

Equivalent?
What is the difference between maximally complete and syntactically complete as defined? Similarly between deductively complete and semantically complete? (Actually there seems to be a misprint because semantically complete is referred to but not defined.) They seem to say the same thing. The page needs some cleaning up. —Preceding unsigned comment added by 81.210.255.97 (talk) 17:01, 17 March 2008 (UTC)

 * I'm not familiar with the terminology of "semantical completeness", but I suspect the property may be meant that is called "strong completeness" in the section on Mathematics. I'm also not sure how common and notable all these variants of the notion of completeness in logic are, since most are equivalent under mild assumptions that would tend to hold in logics unless they are specifically constructed to form a counterexample. Following the definitions of the article, maximal completeness implies syntactic completeness, but the converse implication does not necessarily hold. Take the logic whose sentences consist of a finite sequence of ¬ symbols followed by the symbol ⊥. The theorems are those sentences that have an odd number of ¬ symbols: {¬⊥, ¬¬¬⊥, ¬¬¬¬¬⊥, ...}. This logic is clearly syntactically complete. But ⊥ is not a theorem, and this sentence is also not a negation and therefore not the negation of any theorem. So the logic is not maximally complete. In general, a necessary condition for maximal completeness is that all unprovable sentences have the form of a negation; you can't have 1 < 0 as a sentence, so to speak. To me this seems to be both an unusual and a useless concept. --Lambiam 09:58, 18 March 2008 (UTC)

 * I see that now the two have been merged. Since I have shown above that the two definitions are not equivalent, the old definition of maximally complete and the new one cannot both be right. --Lambiam 00:50, 29 March 2008 (UTC)

In other articles of Wikipedia (eg Predicate Logic) there is reference to syntactic and semantic completeness: the former means that one can always prove P or NOT P; the second means that every statement that holds universally (in every model) can be proved. Are these equivalent? under what assumptions? —Preceding unsigned comment added by 92.50.98.91 (talk) 09:26, 1 April 2008 (UTC)

 * In general they are not equivalent. There is a problem with the notion of "holding universally". You have to fix certain symbols as constants. Otherwise, suppose we have a logic with 0-ary symbols ⊥ and ⊤. We can interpret ⊥ and ⊤ as, respectively, "false" and "true" in some models, but as "true" and "false" in other models. That means that basically no sentence holds in all models. If the logic is semantically sound, not even ⊤ is a theorem. Therefore we must fix certain symbols as logical constants, which however means that our pronouncements can no longer be about completely arbitrary logics. In the following I only use customary fixed interpretations: ⊥ means "false", ⊤ means "true", and ¬ means "not".
 * Take the logic whose formal language consists of only the sentences ⊥ and ⊤, and nothing else. The logic has a single axiom, ⊤, and no derivation rules. This logic cannot be syntactically complete, since neither ⊥ nor ¬⊥ is a theorem – the latter is not even a sentence of the language! But the system is semantically sound and complete.
 * If the logic is sound and syntactically complete, then it is also semantically complete: every true sentence is a theorem. The argument is as follows. Let P be an arbitrary true sentence. Then ¬P cannot be a theorem, since the system is sound. But then instead P is a theorem, since the system is syntactically complete.
 * Without the requirement of soundness, the implication does not follow. Take the logic whose sentences consist of a finite sequence of ¬ symbols followed by the symbol ⊥. The theorems are those sentences that have an even number of ¬ symbols: {⊥, ¬¬⊥, ¬¬¬¬⊥, ...}. This logic is clearly syntactically complete. The true sentences are those with an odd number of ¬ symbols, but none of these is a theorem, so this logic is semantically incomplete. It is also very unsound. --Lambiam 01:08, 2 April 2008 (UTC)

Please disambiguate this
Below follows a list of articles about some form of completion or completeness. Note that I did not check all of them to see whether it is appropriate to treat them here. --Lambiam 16:51, 20 March 2008 (UTC)

 * AI-complete
 * ASR-complete
 * Almost complete
 * Bounded complete poset
 * Chain complete
 * Co-NP-complete
 * Co-RE-complete
 * Command line completion
 * Complete (album)
 * Complete (box set)
 * Complete (complexity)
 * Complete Boolean algebra
 * Complete Heyting algebra
 * Complete active space
 * Complete algebraic variety
 * Complete bipartite graph
 * Complete category
 * Complete coloring
 * Complete contract
 * Complete economic integration
 * Complete game

 * Complete graph
 * Complete group
 * Complete homogeneous symmetric polynomial
 * Complete information
 * Complete intersection
 * Complete lattice
 * Complete market
 * Complete measure
 * Complete metric space
 * Complete mixing
 * Complete numbering
 * Complete partial order
 * Complete protein
 * Complete quadrangle
 * Complete quotient
 * Complete set of commuting observables
 * Complete set of invariants
 * Complete theory
 * Completeness (cryptography)
 * Completeness (order theory)
 * Completeness (statistics)

 * Completion (ring theory)
 * Early completion
 * Feature complete
 * Functional completeness
 * Gödel's completeness theorem
 * Hamiltonian completion
 * Knuth-Bendix completion algorithm
 * Line completion
 * Model complete theory
 * NL-complete
 * NP-complete
 * P-complete
 * PSPACE-complete
 * Pattern completion
 * Sharp-P-complete
 * Strongly NP-complete
 * Turing completeness
 * Weakly NP-complete
 * Word completion

Math v logic again
L, Do you really believe that it is not generally true that:
 * "In mathematics, the notion of completeness is related to completeness in logic."

It seems that there is a tendency to write-out everything that connects math to logic. This is the math-centric thing I am always talking about.

It's another small point, but over time the consequences of this tendency have accumulated. Pontiff Greg Bard (talk) 22:59, 28 March 2008 (UTC)

 * To the extent that everything in mathematics is related to logic, it is true that the notion of (say) generalized function in mathematics is related to logic. However, that does not imply that the notion of generalized function in mathematics is related to generalized function in logic. In general, it is a nonsequitur to conclude from the fact that field A is related to field B, to the relationship of equally named concepts in these fields. The various things that mathematicians have called "complete", "completion" or "completeness" have hardly any relationship to each other beyond the common human-language meaning of complete. How does completeness of a measure relate to completeness of a formal system? About to the same extent as it relates to completeness of a dinner set. --Lambiam 01:13, 29 March 2008 (UTC)

yet another kind of completeness
The diode logic article mentions that "diode-resistor logic ... is not a complete logic family." Is there already an article that discusses the various kinds of "complete logic family", and what makes them complete? Perhaps under some other name? Or should I start such an article? --68.0.124.33 (talk) 04:32, 2 October 2008 (UTC)

"Extreme Completeness"
I removed (twice now) the following text:

 * A formal system is extremely complete or complete in the extreme sense iff every sentence is a theorem. Not all formal systems are intended to express "truths" or "falsehoods," however for those that do an extremely complete formal system is the same as an inconsistent formal system.

Until or unless a citation for this particular meaning of 'extreme completeness' is forthcoming, this text doesn't belong in the article. Zero sharp (talk) 01:33, 30 January 2009 (UTC)

The appropriate thing to do in cases like this is place a citation tag, not delete. That is what those tags are for. It would be nice if people looking for certain terms could find them -- even if certain special people don't use them. Pontiff Greg Bard (talk) 02:43, 30 January 2009 (UTC)
 * I eagerly await your citation, which I'm sure you just didn't have right at hand when you were inserting your 'special' usage of the term. Zero sharp (talk) 07:51, 30 January 2009 (UTC)

The formulation is inappropriate anyway. Every sentence being a theorem is a standard definition of an inconsistent deductive system going back at least to Tarski. It has nothing to do with expressing truth or falsehood, and it is a mainstream usage. Even if Gregbard manages to dig a reference for his term, the standard term should come first, and not vice versa. — Emil J. 10:53, 30 January 2009 (UTC)

 * Quelle surprise, no citation, no hits on google for anything other than this page or mirrors of it for the phrase 'extremely complete', therefore removing (for the third time now) as unsourced neologism. Zero sharp (talk) 22:32, 12 February 2009 (UTC)

Functional Analysis
I have my problems with the paragraph

If V is separable, it follows that any vector in V can be written as a (possibly infinite) linear combination of vectors from S.

I doubt that the statement is correct. Take for example the prominent separable Banach space V:=C[0,1], the space of continuous real valued functions on the unit interval [0,1] with the topology of uniform convergence and take S:={1,X,X^2, ...} to be set of all monomials. Then, by Weierstrass Approximation Theorem, S is a complete subset of V. However, an infinite linear combination of monomials is a power series. And a power series which converges always gives you a differentiable function (even a real analytic function). But there are functions in C[0,1] which are not differentiable. So, the statement must be false. Unless I dont understant the statement correctly. I hope, someone can explain this.--131.234.106.197 (talk) 17:05, 23 February 2011 (UTC)

Definition of an inconsistent system
I think the current definition of inconsistency is misleading in one case and wrong in others: "A formal system is inconsistent if and only if every sentence is a theorem."

This equivalence holds in some systems, e.g., classical first-order logic, but not in others, e.g., paraconsistent logic. Even in the systems where it holds, in all of the dozens of books that I have read, this fact is proven as a theorem and even has special names, e.g., the inconsistency effect or principle of explosion. I think the definition should be changed to agree with usual practice: a theory or formal system is inconsistent iff some formula and its negation are both theorems. Also, on the stricter logical meaning of "sentence" (a formula with no free variables), the equivalence as stated above is not as strong as it could be because it holds for all formulas. I will gladly change the definition if no one has objections. Cheers, Honestrosewater (talk) 05:06, 15 January 2012 (UTC)

 * I'm not even sure a definition of inconsistency is needed here since a) an article about completeness and b) where consistency it is used in the definitions of completeness, it is linked to the page on consistency. I'll remove it. mjog (talk) —Preceding undated comment added 23:28, 9 January 2013 (UTC)

"if and only if"
I removed "and only if" from the three main logical definitions of completeness since this implies soundness is required. If it was indeed "iff", then the correct symbolic version of, say semantic completeness, would actually be: $$ \models_{\mathcal S} \varphi\ \leftrightarrow\ \vdash_{\mathcal S} \varphi$$, a formulation which is which is not terribly useful in a discussion of completeness. mjog (talk) 23:43, 9 January 2013 (UTC)
 * The “and only if” should be removed as definitions should use plain “if” per MOS:MATH, nevertheless your explanation makes no sense at all. The symbolic translation of “A formal system S is semantically complete if and only if every tautology of S is a theorem of S” is
 * $$\mathrm{Complete}(S)\mathrel{\color{red}\leftrightarrow}\forall\varphi\,(\models_S\varphi\to{}\vdash_S\varphi),$$
 * where I’ve highlighted the “if and only if” part, and similarly for the other definitions. As you can see, the equivalence you removed is in a different place than you claim, and is completely harmless.—Emil J. 13:15, 10 January 2013 (UTC)
 * Ah yes, you're absolutely right. Perhaps that confusion is part of the reason MOS:MATH suggests using a plain "if". mjog (talk) 22:53, 10 January 2013 (UTC)

Assessment comment
Substituted at 19:53, 1 May 2016 (UTC)

title: Talk:Completeness


text:
Darth Vader

Darth Vader is a fictional character in the Star Wars franchise created by George Lucas. He was first introduced in the original film trilogy as one of the leaders of the Galactic Empire. The prequel trilogy chronicles his transformation from the Jedi Knight Anakin Skywalker into the Sith Lord Darth Vader. His metamorphosis begins when he is lured to the dark side of the Force by Chancellor Palpatine, who later becomes Emperor. After a lightsaber battle with his former mentor Obi-Wan Kenobi, Vader is severely injured and is transformed into a cyborg. He serves Palpatine for over two decades, hunting down the remaining Jedi and attempting to crush the Rebel Alliance. When Palpatine tries to kill Vader's son, Luke Skywalker, the Sith Lord turns against his master and destroys him. Vader is the husband of Padmé Amidala, the father of Luke and his twin sister Leia Organa, and the grandfather of Ben Solo.

David Prowse physically portrays Vader in the original trilogy, while James Earl Jones provides his voice in all of the films and some television series. Jake Lloyd and Hayden Christensen portray Anakin in the prequel trilogy, and Christensen also plays him in the series Obi-Wan Kenobi (2022) and Ahsoka (2023). In the standalone film Rogue One (2016), Vader is portrayed by Spencer Wilding and Daniel Naprous. The character also appears in novels, comics, and video games. He has become an iconic villain of cinema.

Darth Vader
As part of the development for the original Star Wars film, Lucas hired the artist Ralph McQuarrie to create conceptual images for the characters. For Vader, Lucas asked McQuarrie to depict a "very tall, dark fluttering figure that had a spooky feeling like it came in on the wind." Because the script described Vader traveling between spaceships, McQuarrie suggested that he should wear a space suit. Lucas agreed, and McQuarrie created Vader's iconic mask by combining a full-face breathing mask with a samurai helmet. A 1975 production painting by McQuarrie depicts Vader engaged in a lightsaber duel with Deak Starkiller, who later became Luke Skywalker. Vader is shown wearing black armor, a flowing cape and a skull-like mask and helmet. This early design was similar to Vader's final appearance.

Working from McQuarrie's concepts, the costume designer John Mollo devised an outfit that combined clerical robes, a motorcycle suit, a German military helmet and a military gas mask. The prop sculptor Brian Muir created the helmet and armor. The sound of Vader's breathing was created by the film's sound designer, Ben Burtt, using modified recordings of a scuba breathing apparatus. The sound effect is trademarked at the U.S. Patent and Trademark Office.

Lucas has provided differing accounts of how the name "Darth Vader" originated. In a 2005 interview with Rolling Stone, he claimed it was a modified version of "Dark Father." On another occasion, he said it was inspired by the phrase "Dark Water". It is also possible that "Darth Vader" originated from the name of Gary Vader, a boy who went to high school with Lucas. In France, Darth Vader's name was changed to Dark Vador starting with Star Wars. He was called Dart Fener In Italian-language versions of Star Wars films until 2015, when his name was reverted to the English version. In Iceland, his name is Svarthöfði, which means "black-head".

Anakin Skywalker
The films Swiss Family Robinson (1960) and Battle of the Bulge (1965) influenced the original Star Wars trilogy, but Lucas's publicist has denied that Anakin Skywalker was named after Ken Annakin, the director of those films. The original surname of Anakin and Luke was "Starkiller", and it remained in the script until a few months into filming Star Wars. It was dropped due to what Lucas called "unpleasant connotations" with Charles Manson, who became a "star killer" in 1969 when he murdered the well-known actress Sharon Tate. Lucas replaced the problematic name "Starkiller" with "Skywalker".

The Phantom Menace introduced the possibility that Anakin could be the Chosen One of an ancient Jedi prophecy, who is destined to bring balance to the Force. Lucas stated in an interview that "Anakin is the Chosen One. Even when Anakin turns into Darth Vader, he is still the Chosen One." Hayden Christensen said of Anakin: "He believes that he's the Chosen One. He's not doing wrong things knowing that it's having a negative impact. So there's that sort of naivety to him...and it makes him more human in a lot of ways."

After completing principal photography for Revenge of the Sith in 2003, Lucas made changes to Anakin's character by rewriting his turn to the dark side. He accomplished this through editing the principal footage and filming new scenes during pickups in London in 2004. In previous versions of the script, Anakin had several reasons for turning to the dark side, including his sincere belief that the Jedi were plotting to seize control of the Republic. Although he retains this belief in the finished film, Lucas's changes emphasized his desire to rescue Padmé from death. Thus, in the theatrical version of Revenge of the Sith, Anakin falls to the dark side primarily to save Padmé.

Anakin's apprentice Ahsoka Tano was introduced in the 2008 animated film The Clone Wars. Giving Anakin responsibility for a Padawan was meant to place the character in a role that forced him to become more cautious and responsible. It was also meant to provide him with insight about his relationship with his own master, Obi-Wan Kenobi, and show how their relationship matured. Anakin's relationship with Ahsoka was seen as an essential story arc spanning both the film and the The Clone Wars television series.

Darth Vader
David Prowse, a 6 ft bodybuilder and actor, portrays Vader in the original trilogy. Prowse was originally offered the role of Chewbacca, but turned it down, as he wanted to play the villain. Bob Anderson, a former Olympic fencer, portrays Vader during lightsaber fight scenes in The Empire Strikes Back and Return of the Jedi. Lucas chose to have a different actor provide Vader's voice, because he felt Prowse's West Country English accent was inappropriate for the character. The director originally considered Orson Welles for the role, but selected James Earl Jones instead after deciding that Welles's voice would be too recognizable to audiences. Jones initially felt his role was too small to warrant recognition, and he chose to be uncredited in Star Wars and The Empire Strikes Back. He was finally credited in Return of the Jedi in 1983.

When filming the scene in The Empire Strikes Back in which Vader confesses he is Luke's father, Prowse was given modified dialogue to read that did not exist in the script. He was known for repeatedly leaking information to the public, and the filmmakers wanted to keep Vader's revelation a secret until the film was released. Prowse was asked to read the line "Obi-Wan Kenobi is your father" instead of "No, I am your father." Only the director, the producers, and Mark Hamill knew the actual line, which was dubbed in later by Jones. Prowse did not know the real line until he viewed the finished film.

Hayden Christensen portrays Vader in Revenge of the Sith, while Brock Peters provides his voice in the Star Wars radio series. Scott Lawrence voices Vader in video games, including the 2019 virtual reality series Vader Immortal. Matt Sloan voices the Sith Lord in both video games and television productions. Both Spencer Wilding and Daniel Naprous portray Vader in Rogue One, with Jones providing the voice. Jones also voices Vader in the Star Wars Holiday Special (1978) and the animated series Star Wars Rebels. In September 2022, it was confirmed that Jones would retire from voicing the character. His voice was digitally recreated by the company Respeecher for use in the series Obi-Wan Kenobi, and he later signed over the rights to his voice for future Star Wars productions.

Anakin Skywalker
Near the end of Return of the Jedi, Luke removes Vader's mask. Although Prowse had portrayed the Sith Lord throughout the trilogy, the filmmakers wanted a more experienced actor to play the unmasked Vader. Sebastian Shaw was selected for the role, which appears as "Anakin Skywalker" in the credits. Shaw's presence on set was kept secret from all but the minimum cast and crew, and Shaw was contractually obligated not to discuss any film secrets with anyone, even his family. In the final scene of the film, Shaw portrays Anakin's Force spirit. His likeness in this scene was replaced with that of Hayden Christensen in the 2004 DVD release.

When The Phantom Menace was being developed, hundreds of actors were auditioned for the role of young Anakin before Jake Lloyd was cast. Rick McCallum, the film's producer, said that Lloyd was "smart, mischievous and love[d] anything mechanical—just like Anakin." When casting the role of 19-year-old Anakin for Attack of the Clones, the filmmakers reviewed about 1,500 candidates before selecting Hayden Christensen. The Canadian actor reprises the role in Revenge of the Sith and in the series Obi-Wan Kenobi and Ahsoka. His performance in Revenge of the Sith garnered him a nomination for the Saturn Award for Best Actor, while his portrayal of Anakin in Obi-Wan Kenobi earned him the Saturn Award for Best Guest Performance in a Streaming Series.

Anakin is voiced by Mat Lucas and Frankie Ryan Manriquez in the 2003 animated micro-series Clone Wars, and is voiced by Kirby Morrow in several television productions. Matt Lanter provides the character's voice in video games and in various television productions, including The Clone Wars, Rebels, Forces of Destiny and Star Wars: Tales. Lanter also voices Anakin in the film version of The Clone Wars. During the second-season finale of Rebels, Lanter's voice is sometimes blended with the voice of James Earl Jones.

Original trilogy
Vader was introduced in Star Wars (1977) as a cyborg commander serving the Galactic Empire. He and Grand Moff Tarkin have been tasked with recovering architectural plans for the Death Star battle station, which were stolen by the Rebel Alliance. Vader captures and interrogates the Rebel leader Princess Leia, who has sent the plans to Vader's former master Obi-Wan Kenobi. During Leia's rescue by Obi-Wan's allies Luke Skywalker and Han Solo, Vader strikes down his mentor in a lightsaber duel. After placing a tracking device aboard Han's ship, Vader locates the Rebel base on Yavin 4. When the Rebels attack the Death Star, Vader pursues Luke in his TIE fighter. Before he can shoot Luke down, Han intervenes and sends Vader's ship spiraling off course, which allows Luke to destroy the Death Star.

In The Empire Strikes Back (1980), Vader becomes obsessed with finding Luke, who is now a Rebel commander. Vader's forces assault the Rebel base on Hoth, but the Rebels escape. Vader convinces the Emperor that Luke could be a valuable ally if he were turned to the dark side of the Force. Vader hires a group of bounty hunters to follow Luke's companions, and compels the Cloud City administrator Lando Calrissian to set a trap for them. After Han, Leia, Chewbacca and C-3PO arrive, Vader tortures and freezes Han in carbonite and gives him to the bounty hunter Boba Fett. When Luke lands on Cloud City to help his friends, Vader overpowers him and severs his hand. He tells Luke that he is his father, and tries to persuade him to join the dark side and help him overthrow the Emperor. Horrified, Luke escapes through an air shaft. Vader telepathically tells Luke that it is his destiny to join the dark side.

Vader and the Emperor supervise the construction of the second Death Star in Return of the Jedi (1983). Believing there is still good in his father, Luke surrenders to Vader in an attempt to bring him back from the dark side. Vader takes his son to the Death Star and brings him before the Emperor, who attempts to seduce him to the dark side. Luke lashes out at the Emperor with his lightsaber, but Vader blocks his strike, and the two of them duel once again. As Luke regains control of his emotions, Vader senses that he has a sister, and threatens to turn her to the dark side if Luke will not submit. Enraged, Luke overpowers Vader and severs his hand. The Emperor then orders Luke to kill Vader and take his place, but Luke refuses.

The Emperor begins torturing Luke with Force lightning, and Luke calls out to his father for help. Vader hesitates, then throws the Emperor down a reactor shaft to his death. Vader is mortally wounded, and Luke carries him to a docking bay, where Imperial forces are evacuating in the face of a Rebel assault. At Vader's request, Luke removes his father's mask and looks upon the face of Anakin Skywalker for the first time. On Endor, Luke burns his father's body on a funeral pyre. As the Rebels celebrate the destruction of the Death Star and the fall of the Empire, Luke sees Anakin's spirit appear alongside the spirits of Obi-Wan and Yoda.

Prequel trilogy
The first film of the prequel trilogy, The Phantom Menace (1999), takes place 32 years before Star Wars. Anakin is a nine-year-old slave living on Tatooine with his mother Shmi. He is a gifted pilot and mechanic, and has built his own protocol droid, C-3PO. The Jedi Master Qui-Gon Jinn meets Anakin after making an emergency landing on Tatooine with Padmé Amidala, the queen of Naboo. Qui-Gon learns that Anakin was conceived without a father and can see the future. He becomes convinced that Anakin is the "Chosen One" of Jedi prophecy who will bring balance to the Force. After winning his freedom in a podrace wager, Anakin departs the planet with Qui-Gon to be trained as a Jedi, leaving his mother behind.

During the journey to Coruscant, Anakin forms a bond with Padmé. Qui-Gon asks the Jedi Council for permission to train Anakin, but they refuse, concerned that the fear he exhibits makes him vulnerable to the dark side. During a conflict with the Trade Federation, Anakin helps end the blockade of Naboo by destroying a control ship. Qui-Gon is mortally wounded in a duel with the Sith Lord Darth Maul, and with his dying breath asks his apprentice Obi-Wan Kenobi to train Anakin. With the Council's reluctant approval, Anakin becomes Obi-Wan's apprentice. Palpatine, the newly elected Chancellor of the Galactic Republic, takes an interest in Anakin and his career as a Jedi.

Attack of the Clones (2002) is set ten years after The Phantom Menace. Anakin has grown powerful but arrogant, and believes that Obi-Wan is holding him back. After rescuing Padmé from an assassination attempt, he travels with her to Naboo as her bodyguard. They begin to fall in love, despite a Jedi Code prohibition against romantic relationships. Sensing that his mother is in danger, Anakin travels with Padmé to Tatooine and finds that she was kidnapped by Tusken Raiders. He locates her at a Tusken campsite, where she dies in his arms. Overcome with grief and rage, Anakin massacres the Tusken tribe. Padmé is disturbed by what he has done, but comforts him nevertheless. Anakin and Padmé then go to Geonosis to aid, only to be captured by the Sith Lord Count Dooku. Facing execution, Anakin and Padmé profess their love for each other. They are saved from death by an army of Jedi and clone troopers, led by the Jedi Masters Mace Windu and Yoda. Anakin and then confront Dooku, but he defeats them both and severs Anakin's arm. After being rescued by Yoda, Anakin is fitted with a robotic arm and marries Padmé in a secret ceremony.Revenge of the Sith (2005) is set three years after Attack of the Clones. Anakin, who is now a Jedi Knight and a hero of the Clone Wars, leads a mission with to rescue Chancellor Palpatine from the Separatist commander General Grievous. The two Jedi again battle Count Dooku, whom Anakin overpowers and then slaughters at Palpatine's urging. Anakin returns to Coruscant to reunite with Padmé, who tells him she is pregnant. Although initially excited, Anakin soon begins to have nightmares about his wife dying in childbirth.

Palpatine appoints Anakin to the Jedi Council as his personal representative, but the Council is suspicious of the Chancellor. They decline to grant Anakin the rank of Jedi Master and instruct him to spy on Palpatine, which upsets Anakin. Later, Palpatine reveals to Anakin that he is the Sith Lord Darth Sidious, the mastermind of the Clone Wars. He suggests that Anakin can prevent Padmé's death by using the dark side of the Force. Anakin reports Palpatine's treachery to Windu, who confronts and subdues the Sith Lord. Desperate to save Padmé, Anakin intervenes on Palpatine's behalf and severs Windu's hand, which allows Palpatine to kill him. Anakin then pledges himself to the Sith, and Palpatine dubs him Darth Vader.

On Palpatine's orders, Vader slaughters all the Jedi in the Jedi Temple, including the children. After learning what her husband has done, a distraught Padmé travels to Mustafar and pleads with him to abandon the dark side, but he refuses. Believing that Padmé and are conspiring against him, Vader uses the Force to strangle his wife into unconsciousness. He then engages in a lightsaber duel that ends with  severing his limbs and leaving him for dead on the banks of a lava flow, where he catches fire and sustains severe burns. Palpatine finds the barely-alive Vader and takes him to Coruscant, where his mutilated body is covered in black armor that keeps him alive. When Vader asks if Padmé is safe, Palpatine lies to him and says that his strangulation killed her, which causes Vader to scream in anguish. At the end of the film, Vader supervises the construction of the first Death Star alongside Palpatine and Tarkin.

The Rise of Skywalker
Anakin's voice is heard briefly in the third film of the sequel trilogy, The Rise of Skywalker (2019). During Rey's confrontation with the resurrected Palpatine, she hears the voices of various deceased Jedi, including Anakin. He encourages her to return balance to the Force.

The Clone Wars (film)
In the 2008 animated film The Clone Wars, Yoda assigns Anakin an apprentice, Ahsoka Tano. Anakin is at first reluctant to accept this responsibility. He calls Ahsoka "Snips" for her "snippy" attitude, while Ahsoka refers to him as "Skyguy". After earning Anakin's respect during a dangerous mission, Ahsoka joins him on a quest to rescue Jabba the Hutt's infant son, Rotta. Her impetuousness both annoys and endears her to Anakin, and he develops a friendly affection towards her.

Rogue One
In the standalone film Rogue One (2016), Vader summons the weapons developer Orson Krennic to his castle on Mustafar. He confronts him about his handling of the Death Star project and the destruction of Jedha City. When Krennic asks Vader for an audience with the Emperor, Vader refuses. At the end of the film, Vader boards a Rebel flagship and kills several Rebel soldiers as he tries unsuccesfully to recover the stolen Death Star plans. Vader's role in the film was different in early versions of the story. In Gary Whitta's original pitch, the Sith Lord appeared on Scarif and slaughtered a Rebel blockade. In another early storyline, Vader killed Krennic for his failure to prevent the Rebels from stealing the Death Star schematics.

The Clone Wars
Anakin is featured in all seasons of The Clone Wars (2008–2014, 2020). As a Jedi Knight, he leads the 501st Legion on missions with both his master Obi-Wan and his apprentice Ahsoka. Some of Anakin's actions taken out of concern for Ahsoka violate the Jedi code, such as torturing prisoners who may know her location. Throughout the series there are references to Anakin's eventual fall to the dark side, including visions of his future as Vader and his disillusionment with the Jedi Council after they wrongly accuse Ahsoka of bombing the Jedi Temple. While Ahsoka is later forgiven after the true culprit is found, she nonetheless chooses to leave the Jedi Order. Anakin appears as Vader in the final scene of the series finale, which occurs after Revenge of the Sith. He investigates the crash site of a Star Destroyer, which was demolished during Order 66. Finding one of Ahsoka's lightsabers among the wreckage, he assumes that his former Padawan has perished.

Star Wars Rebels
Vader appears in the animated series Star Wars Rebels (2014–2018), which takes place fourteen years after the conclusion of The Clone Wars. The Sith Lord makes minor appearances throughout the first season, and plays a larger role in the second season. At the beginning of the series, he leads a squad of Force-sensitive Imperial Inquisitors who kill Jedi and children. He dispatches the Grand Inquisitor to hunt a Rebel cell on Lothal, and later arrives personally to deal with the Rebel threat after the Inquisitor is killed.

In the second-season premiere, Vader orchestrates the murder of Imperial Minister Maketh Tua, who tried to defect to the Rebellion, and confronts the two Jedi Kanan Jarrus and Ezra Bridger. When Vader attacks the fleet of the Phoenix Squadron, he discovers that Ahsoka is still alive and has joined the Rebel Alliance. She is overwhelmed when she recognizes Anakin under a "layer of hate". The Emperor then orders Vader to send another Inquisitor to capture her. Later in the season, Ahsoka has a vision in which Anakin blames her for his fall to the dark side. In the season finale, Ahsoka duels with Vader inside a Sith Temple. As the episode concludes, Vader emerges from the ruins of the temple, while Ahsoka's fate is left unknown.

Forces of Destiny
Anakin appears in multiple episodes of the animated web series Forces of Destiny (2017–2018).

Obi-Wan Kenobi
Hayden Christensen portrays both Anakin and Vader in the 2022 miniseries Obi-Wan Kenobi. The series reveals that for a decade after their duel on Mustafar, Obi-Wan believed his fallen apprentice to be dead. While attempting to draw out of hiding, the Imperial Inquisitor Reva Sevander tells him that Anakin is still alive. Vader begins hunting, which eventually leads them to duel again. Although Vader initially overpowers his former master, recovers his strength and wounds Vader multiple times. He slashes open Vader's helmet to partially reveal his face, then leaves him, weakened and wheezing. Flashback sequences in the series depict Anakin training under in the years preceding the Clone Wars, as well as a newly-minted Vader carrying out the massacre at the Jedi Temple.

Ahsoka
Hayden Christensen portrays Anakin in Ahsoka (2023), which takes place after the original trilogy. Anakin appears in spirit-form to his former apprentice Ahsoka in the World Between Worlds, an ethereal realm that exists outside of time and space. He leads her through visions of their shared past together, including her training, their battles during the Clone Wars, her departure from the Jedi Order and his fall to the dark side. Industrial Light and Magic used "de-aging" technology to make the 42-year-old Christensen appear younger.

Video games
Vader is featured in the three-episode virtual reality game series Vader Immortal, which is set between Revenge of the Sith and Rogue One. The first episode became available with the launch of the Oculus Quest virtual reality headset in May 2019, while the last was released in November of the same year. The series was later released for the Oculus Rift. In August 2020, all three episodes were released for PlayStation VR.

Vader makes a brief appearance at the end of Jedi: Fallen Order (2019). He kills the Second Sister for her failure to secure a Jedi Holocron that could lead the Empire to a number of Force-sensitive children. He then attempts to personally take the Holocron from Cal Kestis, who barely manages to escape. Vader returns as a boss in the sequel, Jedi: Survivor (2023), where he leads an Imperial assault on a Jedi hideout on the planet Jedha. He duels Cere Junda, whom he manages to slay after a prolonged battle.

Both Vader and Anakin are playable characters in every Lego Star Wars video game. Vader is a playable character and a boss in Disney Infinity 3.0, and can be unlocked as a playable character for a limited time in Disney Magic Kingdoms. A bird version of Vader appears as a playable character and a boss in Angry Birds Star Wars and its sequel.

Novels
Star Wars: Lords of the Sith was one of four canon novels released between 2014 and 2015. In it, Vader and Palpatine find themselves hunted by revolutionaries on the planet Ryloth.

Comics
The 25-issue Marvel comic series Darth Vader (2015–2016) focuses on the Sith Lord in the aftermath of the Death Star's destruction, as well as his life after learning about his son's existence. The series takes place parallel to the 2015 series Star Wars, in which Vader and Luke meet; the two series have a crossover titled Vader Down. A continuation series set between The Empire Strikes Back and Return of the Jedi debuted in 2020. The first few issues focus on Vader exacting revenge on those who concealed Luke; he also visits Padmé's tomb on Naboo and encounters her handmaidens. A subsequent story arc depicts Vader being tested by the Emperor. The five-issue series Obi-Wan & Anakin (2016) depicts the lives of the two Jedi between The Phantom Menace and Attack of the Clones.

Between 2017 and 2018, Charles Soule wrote a prequel-era series, also called Darth Vader (sometimes subtitled Dark Lord of the Sith). It begins immediately after Vader wakes up in his armor at the end of Revenge of the Sith and explores his emotional transformation upon learning of Padmé's death, his adjustment to his mechanical suit, how he creates his red-bladed lightsaber, and his hunting of Jedi in the Inquisitor program. Its final arc, which depicts the construction of Vader's fortress on Mustafar, implies that Palpatine used the Force to conceive Anakin in utero, as some had theorized that Revenge of the Sith indicates. A Lucasfilm story group member later clarified that "This is all in Anakin's head".

A five-issue limited series titled Vader: Dark Visions, was released in 2019. Vader Down writer Jason Aaron wrote part of the miniseries Darth Vader: Black, White & Red, an extension of a Marvel event highlighting fan-favorite characters.

Star Wars Legends
Following the acquisition of Lucasfilm by The Walt Disney Company in 2012, most of the licensed Star Wars novels and comics produced between 1977 and 2014 were rebranded as Star Wars Legends and declared non-canon to the franchise. The Legends works comprise a separate narrative universe.

Books
Vader is featured prominently in novels set in the Star Wars universe. In the 1978 novel Splinter of the Mind's Eye by Alan Dean Foster, Vader meets Luke for the first time and engages him in a lightsaber duel that ends with Luke cutting off Vader's arm and Vader falling into a deep pit. Shadows of the Empire (1996) reveals that Vader is conflicted about trying to turn his son to the dark side, and knows deep down that he still has good in him.

Vader's supposedly indestructible glove is the MacGuffin of the young-reader's book The Glove of Darth Vader (1992). Anakin Skywalker's redeemed spirit appears in The Truce at Bakura (1993), set a few days after the end of Return of the Jedi. He appears to Leia, imploring her forgiveness. Leia condemns Anakin for his crimes and banishes him from her life. He promises that he will be there for her when she needs him, and disappears. In Tatooine Ghost (2003), Leia learns to forgive her father after learning about his childhood as a slave and his mother's traumatic death. In The Unifying Force (2003), Anakin tells his grandson Jacen Solo to "stand firm" in his battle with the Supreme Overlord of the Yuuzhan Vong.

Upon the release of the prequel films, the Expanded Universe grew to include novels about Vader's former life as Anakin. Greg Bear's 2000 novel Rogue Planet and Jude Watson's Jedi Quest series chronicle Anakin's early missions with Obi-Wan, while James Luceno's 2005 novel Labyrinth of Evil, set during the Clone Wars, depicts Anakin battling Separatist commander General Grievous. In Luceno's Dark Lord: The Rise of Darth Vader (2005), set a few months after the events of Revenge of the Sith, Vader disavows his identity as Anakin as he hunts down surviving Jedi and cements his position in the Empire.

In the Dark Nest trilogy (2005), Luke and Leia uncover old recordings of their parents in R2-D2's memory drive; for the first time, they see their own birth and their mother's death, as well as their father's corruption to the dark side. In Bloodlines (2006), Han and Leia's son Jacen—who has turned to the dark side—uses the Force to envision Vader slaughtering the children at the Jedi Temple.

Vader also appears in a series of tongue-in-cheek children's books by Jeffrey Brown. In Brown's series, a hapless Vader sets out to be a father to a young Luke and Leia, with some scenes portraying light-hearted versions of their darker film counterparts. For example, one scene shows Vader, Luke and Leia at the carbonite freezing chamber on Bespin, with Vader pronouncing the freezer adequate for making ice cream.

Comics
Vader appears in several comic books such as Marvel Comics' Star Wars (1977–1986). In Dark Empire II, he is revealed to have had a castle on the planet Vjun. Anakin Skywalker is a major character in Dark Horse Comics' Star Wars: Republic series (1998–2006). In Boba Fett: Enemy of the Empire (1999), Vader hires Fett a few years before the events of A New Hope. In Vader's Quest (1999), set soon after A New Hope, the dark lord encounters Luke for the first time. Star Wars: Empire (2002–2005) spans from about a year before A New Hope to several months afterwards. Anakin and Vader appear in the non-canonical Star Wars Tales (1999–2005); in the story Resurrection, Darth Maul is resurrected and faces Vader in battle.

Vader-centric comics released and set just after Revenge of the Sith include Dark Times (2006–2013), Darth Vader and the Lost Command (2011), Darth Vader and the Ghost Prison (2012), and Darth Vader and the Cry of Shadows (2013–14).

Clone Wars
Anakin is featured in all three seasons of the Clone Wars micro-series (2003–2005), which takes place shortly after the conclusion of Attack of the Clones. Anakin becomes a Jedi Knight and is quickly promoted to General of the Republic, due in part to Palpatine's influence. Among other missions, he fights a duel with Dooku's apprentice Asajj Ventress, helps Obi-Wan capture a Separatist-controlled fortress, and rescues the Jedi Master Saesee Tiin during a space battle. During the third season, Anakin frees a planet's indigenous species from Separatist control and sees a cryptic vision of his future as Darth Vader. In the series finale, Anakin and Obi-Wan embark on a mission to rescue Palpatine from General Grievous, which leads into the opening of Revenge of the Sith. The series was removed from canon in 2014 and placed in the Legends universe.

Video games
Vader plays a central role in the Legends game Star Wars: The Force Unleashed (2008), where he is playable in the first level and later appears as a boss. He also appears in the sequel, Star Wars: The Force Unleashed II (2010), as the final boss.

Other appearances
The Star Wars Holiday Special, a television special broadcast by CBS in 1978, features a brief appearance of Darth Vader, who appears on-screen speaking with Imperial officer "Chief Bast" in footage cut from the original 1977 film. The sequence is dubbed with new dialogue, performed by James Earl Jones. In the story, Vader colludes with Boba Fett to entrap the Rebels.

The character appears in various Lego Star Wars shorts, voiced by Matt Sloan as Vader and by Kirby Morrow as Anakin.

Darth Vader features in the 1981 radio drama adaptation of Star Wars, voiced by the actor Brock Peters. Vader makes his first appearance on the planet Ralltiir, where he treats Princess Leia with suspicion. In later extended scenes, he is heard interrogating and torturing Leia on board his Star Destroyer and aboard the Death Star.

Analysis
The French psychiatrist Eric Bui and his colleagues have considered Vader to be a useful example for explaining borderline personality disorder to medical students. Anakin's origin story in The Phantom Menace has been compared to signifiers of African American racial identity, particularly his being a slave, and his dissatisfaction with his life has been compared to Siddartha's before he became Gautama Buddha.

Cultural impact
In 2003, the American Film Institute listed Vader as the third greatest movie villain in cinema history on AFI's 100 Years...100 Heroes & Villains, behind Hannibal Lecter and Norman Bates. In 2010, IGN ranked Darth Vader 25th in the "Top 100 Videogame Villains". His role as a tragic hero in the saga has also met with positive reviews. Contrarily, in 1977, a New Journal and Guide writer criticized the lack of racial diversity in the original Star Wars film, pointing out that "the force of evil ... is dressed in all black and has the voice of a black man." George Lucas felt hurt at such accusations.

Vader is parodied as "Dark Helmet" (Rick Moranis) in the Star Wars parody Spaceballs (1987). One of the primary antagonists of Final Fantasy IV (1991), Golbez, was stated by game creator Takashi Tokita to be based on Vader. A Mexican church advised Christians against seeing The Phantom Menace because it portrays Anakin as a Christ figure.

The slime-mold beetle Agathidium vaderi is named after Vader, as is the louse Ricinus vaderi. A grotesque of Darth Vader looms over the east face of the Washington National Cathedral's northwest tower.

Many commentators and comedians have also evoked Vader's visage to satirize politicians and other public figures, and several American political figures have been unflatteringly compared to the character. In response to Ronald Reagan's proposed Strategic Defense Initiative (dubbed "Star Wars" by his political opponents), German news magazine Der Spiegel portrayed the president wearing Vader's helmet on its cover in 1984. In 2005, Al Gore referred to Tele-Communications Inc.'s John C. Malone as the "Darth Vader of cable", and political strategist Lee Atwater was known by his political enemies as "the Darth Vader of the Republican Party". Native American artist Bunky Echohawk portrayed General George Armstrong Custer as Vader in his painting Darth Custer. In 2015, a statue of Vladimir Lenin in Odesa, Ukraine, was converted into one of Vader due to a law on decommunization. Former Vice President of the United States Dick Cheney has been compared to Darth Vader after he was quoted during a discussion on the war on terror saying, "I suppose, sometimes, people look at my demeanor and say, 'Well, he's the Darth Vader of the administration.'" This lead to him being referred to as "Darth Cheney" by Jon Stewart and Stephen Colbert. This comparison was followed by George Lucas stating that Cheney is more akin to Palpatine, and that a better stand-in for Vader would be George W. Bush.

In Ukraine, the Internet Party of Ukraine has had multiple people run for election under the name Darth Vader.

The Fedayeen Saddam, an Iraqi paramilitary organisation, was issued with fiber glass Darth Vader-style helmets from 1995, apparently at the instigation of their commander, Uday Hussein, who was said to have been an avid Star Wars fan. A number of them were brought to the United States and the United Kingdom as souvenirs following the 2003 invasion of Iraq.

In 2019, an original Vader helmet from The Empire Strikes Back was sold for $900,000 in an online auction.

title: Darth Vader