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Axiom schema of specification

In many popular versions of axiomatic set theory, the axiom schema of specification, also known as the axiom schema of separation (Aussonderung Axiom), subset axiom  or axiom schema of restricted comprehension is an axiom schema. Essentially, it says that any definable subclass of a set is a set.

Some mathematicians call it the axiom schema of comprehension, although others use that term for unrestricted comprehension, discussed below.

Because restricting comprehension avoided Russell's paradox, several mathematicians including Zermelo, Fraenkel, and Gödel considered it the most important axiom of set theory.

Statement
One instance of the schema is included for each formula $$\varphi(x)$$ in the language of set theory with $$x$$ as a free variable. So $$S$$ does not occur free in $$\varphi(x)$$. In the formal language of set theory, the axiom schema is:
 * $$\forall A \, \exists S \, \forall x \, \big( x \in S \iff (x \in A \wedge \varphi(x)) \big)$$

or in words:
 * Let $$\varphi(x)$$ be a formula. For every set $$A$$ there exists a set $$S$$ that consists of all the elements $$x \in A$$ such that $$\varphi(x)$$ holds.

Note that there is one axiom for every such predicate $$\varphi(x)$$; thus, this is an axiom schema.

To understand this axiom schema, note that the set $$S$$ must be a subset of A. Thus, what the axiom schema is really saying is that, given a set $$A$$ and a predicate $$\varphi(x)$$, we can find a subset $$S$$ of A whose members are precisely the members of A that satisfy $$\varphi(x)$$. By the axiom of extensionality this set is unique. We usually denote this set using set-builder notation as $$S = \{x\in A | \varphi(x) \}$$. Thus the essence of the axiom is:
 * Every subclass of a set that is defined by a predicate is itself a set.

The preceding form of separation was introduced in 1930 by Thoralf Skolem as a refinement of a previous, non-first-order form by Zermelo. The axiom schema of specification is characteristic of systems of axiomatic set theory related to the usual set theory ZFC, but does not usually appear in radically different systems of alternative set theory. For example, New Foundations and positive set theory use different restrictions of the axiom of comprehension of naive set theory. The Alternative Set Theory of Vopenka makes a specific point of allowing proper subclasses of sets, called semisets. Even in systems related to ZFC, this scheme is sometimes restricted to formulas with bounded quantifiers, as in Kripke–Platek set theory with urelements.

Relation to the axiom schema of replacement
The axiom schema of specification is implied by the axiom schema of replacement together with the axiom of empty set.

The axiom schema of replacement says that, if a function $$f$$ is definable by a formula $$\varphi(x, y, p_1, \ldots, p_n)$$, then for any set $$A$$, there exists a set $$B = f(A) = \{ f(x) \mid x \in A \}$$:

 * $$\begin{align}

&\forall x \, \forall y \, \forall z \, \forall p_1 \ldots \forall p_n [ \varphi(x, y, p_1, \ldots, p_n) \wedge \varphi(x, z, p_1, \ldots, p_n) \implies y = z ] \implies \\ &\forall A \, \exists B \, \forall y ( y \in B \iff \exists x ( x \in A \wedge \varphi(x, y, p_1, \ldots, p_n) ) ) \end{align}$$.

To derive the axiom schema of specification, let $$\varphi(x, p_1, \ldots, p_n)$$ be a formula and $$z$$ a set, and define the function $$f$$ such that $$f(x) = x$$ if $$\varphi(x, p_1, \ldots, p_n)$$ is true and $$f(x) = u$$ if $$\varphi(x, p_1, \ldots, p_n)$$ is false, where $$u \in z$$ such that $$\varphi(u, p_1, \ldots, p_n)$$ is true. Then the set $$y$$ guaranteed by the axiom schema of replacement is precisely the set $$y$$ required in the axiom schema of specification. If $$u$$ does not exist, then $$f(x)$$ in the axiom schema of specification is the empty set, whose existence (i.e., the axiom of empty set) is then needed.

For this reason, the axiom schema of specification is left out of some axiomatizations of ZF (Zermelo-Frankel) set theory, although some authors, despite the redundancy, include both. Regardless, the axiom schema of specification is notable because it was in Zermelo's original 1908 list of axioms, before Fraenkel invented the axiom of replacement in 1922. Additionally, if one takes ZFC set theory (i.e., ZF with the axiom of choice), removes the axiom of replacement and the axiom of collection, but keeps the axiom schema of specification, one gets the weaker system of axioms called ZC (i.e., Zermelo's axioms, plus the axiom of choice).

Unrestricted comprehension
The axiom schema of unrestricted comprehension reads:

$$\forall w_1,\ldots,w_n \, \exists B \, \forall x \, ( x \in B \Leftrightarrow \varphi(x, w_1, \ldots, w_n) )$$

that is:

This set $B$ is again unique, and is usually denoted as ${x : φ(x, w1, ..., wb)}.$

This axiom schema was tacitly used in the early days of naive set theory, before a strict axiomatization was adopted. However, it was later discovered to lead directly to Russell's paradox, by taking $φ(x)$ to be $¬(x ∈ x)$ (i.e., the property that set $φ$ is not a member of itself). Therefore, no useful axiomatization of set theory can use unrestricted comprehension. Passing from classical logic to intuitionistic logic does not help, as the proof of Russell's paradox is intuitionistically valid.

Accepting only the axiom schema of specification was the beginning of axiomatic set theory. Most of the other Zermelo–Fraenkel axioms (but not the axiom of extensionality, the axiom of regularity, or the axiom of choice) then became necessary to make up for some of what was lost by changing the axiom schema of comprehension to the axiom schema of specification – each of these axioms states that a certain set exists, and defines that set by giving a predicate for its members to satisfy, i.e. it is a special case of the axiom schema of comprehension.

It is also possible to prevent the schema from being inconsistent by restricting which formulae it can be applied to, such as only stratified formulae in New Foundations (see below) or only positive formulae (formulae with only conjunction, disjunction, quantification and atomic formulae) in positive set theory. Positive formulae, however, typically are unable to express certain things that most theories can; for instance, there is no complement or relative complement in positive set theory.

In NBG class theory
In von Neumann–Bernays–Gödel set theory, a distinction is made between sets and classes. A class $B$ is a set if and only if it belongs to some class $x$. In this theory, there is a theorem schema that reads $$\exists D \forall C \, ( [ C \in D ] \iff [ P (C) \land \exists E \, ( C \in E ) ] ) \,,$$

that is,

provided that the quantifiers in the predicate $C$ are restricted to sets.

This theorem schema is itself a restricted form of comprehension, which avoids Russell's paradox because of the requirement that $E$ be a set. Then specification for sets themselves can be written as a single axiom $$\forall D \forall A \, ( \exists E \, [ A \in E ] \implies \exists B \, [ \exists E \, ( B \in E ) \land \forall C \, ( C \in B \iff [ C \in A \land C \in D ] ) ] ) \,,$$

that is,

or even more simply

In this axiom, the predicate $D$ is replaced by the class $C$, which can be quantified over. Another simpler axiom which achieves the same effect is $$\forall A \forall B \, ( [ \exists E \, ( A \in E ) \land \forall C \, ( C \in B \implies C \in A ) ] \implies \exists E \, [ B \in E ] ) \,,$$

that is,

In higher-order settings
In a typed language where we can quantify over predicates, the axiom schema of specification becomes a simple axiom. This is much the same trick as was used in the NBG axioms of the previous section, where the predicate was replaced by a class that was then quantified over.

In second-order logic and higher-order logic with higher-order semantics, the axiom of specification is a logical validity and does not need to be explicitly included in a theory.

In Quine's New Foundations
In the New Foundations approach to set theory pioneered by W. V. O. Quine, the axiom of comprehension for a given predicate takes the unrestricted form, but the predicates that may be used in the schema are themselves restricted. The predicate ($D$ is not in $C$) is forbidden, because the same symbol $P$ appears on both sides of the membership symbol (and so at different "relative types"); thus, Russell's paradox is avoided. However, by taking $P(C)$ to be $(C = C)$, which is allowed, we can form a set of all sets. For details, see stratification.

title: Axiom schema of specification


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Axiom schema of replacement

In set theory, the axiom schema of replacement is a schema of axioms in Zermelo–Fraenkel set theory (ZF) that asserts that the image of any set under any definable mapping is also a set. It is necessary for the construction of certain infinite sets in ZF.

The axiom schema is motivated by the idea that whether a class is a set depends only on the cardinality of the class, not on the rank of its elements. Thus, if one class is "small enough" to be a set, and there is a surjection from that class to a second class, the axiom states that the second class is also a set. However, because ZFC only speaks of sets, not proper classes, the schema is stated only for definable surjections, which are identified with their defining formulas.

Statement
Suppose $$P$$ is a definable binary relation (which may be a proper class) such that for every set $$x$$ there is a unique set $$y$$ such that $$P(x,y)$$ holds. There is a corresponding definable function $$F_P$$, where $$F_P(x)=y$$ if and only if $$P(x,y)$$. Consider the (possibly proper) class $$B$$ defined such that for every set $$y$$, $$y\in B$$ if and only if there is an $$x\in A$$ with $$F_P(x)=y$$. $$B$$ is called the image of $$A$$ under $$F_P$$, and denoted $$F_P[A]$$ or (using set-builder notation) $$\{F_P(x):x\in A\}$$.

The axiom schema of replacement states that if $$F$$ is a definable class function, as above, and $$A$$ is any set, then the image $$F[A]$$ is also a set. This can be seen as a principle of smallness: the axiom states that if $$A$$ is small enough to be a set, then $$F[A]$$ is also small enough to be a set. It is implied by the stronger axiom of limitation of size.

Because it is impossible to quantify over definable functions in first-order logic, one instance of the schema is included for each formula $$\phi$$ in the language of set theory with free variables among $$w_1,\dotsc,w_n,A,x,y$$; but $$B$$ is not free in $$\phi$$. In the formal language of set theory, the axiom schema is:
 * $$\begin{align}

\forall w_1,\ldots,w_n \, \forall A \, ( [ \forall x \in A &\, \exists ! y \, \phi(x, y, w_1, \ldots, w_n, A) ]\ \Longrightarrow\ \exists B \, \forall y \, [y \in B \Leftrightarrow \exists x \in A \, \phi(x, y, w_1, \ldots, w_n, A) ] ) \end{align}$$

For the meaning of $$\exists!$$, see uniqueness quantification.

For clarity, in the case of no variables $$w_i$$, this simplifies to:
 * $$\begin{align}

\forall A \, ( [ \forall x \in A &\, \exists ! y \, \phi(x, y, A) ]\ \Longrightarrow\ \exists B \, \forall y \, [y \in B \Leftrightarrow \exists x \in A \, \phi(x, y, A) ] ) \end{align}$$

So whenever $$\phi$$ specifies a unique $$x$$-to-$$y$$ correspondence, akin to a function $$F$$ on $$A$$, then all $$y$$ reached this way can be collected into a set $$B$$, akin to $$F[A]$$.

Applications
The axiom schema of replacement is not necessary for the proofs of most theorems of ordinary mathematics. Indeed, Zermelo set theory (Z) already can interpret second-order arithmetic and much of type theory in finite types, which in turn are sufficient to formalize the bulk of mathematics. Although the axiom schema of replacement is a standard axiom in set theory today, it is often omitted from systems of type theory and foundation systems in topos theory.

At any rate, the axiom schema drastically increases the strength of ZF, both in terms of the theorems it can prove - for example the sets shown to exist - and also in terms of its proof-theoretic consistency strength, compared to Z. Some important examples follow:

 * Using the modern definition due to von Neumann, proving the existence of any limit ordinal greater than ω requires the replacement axiom. The ordinal number ω·2 = ω + ω is the first such ordinal. The axiom of infinity asserts the existence of an infinite set ω = {0, 1, 2, ...}. One may hope to define ω·2 as the union of the sequence {ω, ω + 1, ω + 2,...}. However, arbitrary such classes of ordinals need not be sets - for example, the class of all ordinals is not a set. Replacement now allows one to replace each finite number n in ω with the corresponding ω + n, and thus guarantees that this class is a set. As a clarification, note that one can easily construct a well-ordered set that is isomorphic to ω·2 without resorting to replacement – simply take the disjoint union of two copies of ω, with the second copy greater than the first – but that this is not an ordinal since it is not totally ordered by inclusion.
 * Larger ordinals rely on replacement less directly. For example, ω1, the first uncountable ordinal, can be constructed as follows – the set of countable well orders exists as a subset of $$P({\mathbb N}\times {\mathbb N})$$ by separation and powerset (a relation on A is a subset of $$A\times A$$, and so an element of the power set $$P(A\times A)$$. A set of relations is thus a subset of $$P(A\times A)$$)). Replace each well-ordered set with its ordinal. This is the set of countable ordinals ω1, which can itself be shown to be uncountable. The construction uses replacement twice; once to ensure an ordinal assignment for each well ordered set and again to replace well ordered sets by their ordinals. This is a special case of the result of Hartogs number, and the general case can be proved similarly.
 * In light of the above, the existence of an assignment of an ordinal to every well-ordered set requires replacement as well. Similarly the von Neumann cardinal assignment which assigns a cardinal number to each set requires replacement, as well as axiom of choice.
 * For sets of tuples recursively defined as $$A^n=A^{n-1}\times A$$ and for large $$A$$, the set $$\{A^n\mid n\in {\mathbb N}\}$$ has too high of a rank for its existence to be provable from set theory with just the axiom of power set, choice and without replacement.
 * Similarly, Harvey Friedman showed that replacement is required to show that Borel games are determined. The proven result is Donald A. Martin's Borel determinacy theorem.
 * ZF with replacement proves the consistency of Z, as the set Vω·2 is a model of Z whose existence can be proved in ZF. The cardinal number $$\aleph_\omega$$ is the first one which can be shown to exist in ZF but not in Z. For clarification, note that Gödel's second incompleteness theorem shows that each of these theories contains a sentence, "expressing" the theory's own consistency, that is unprovable in that theory, if that theory is consistent - this result is often loosely expressed as the claim that neither of these theories can prove its own consistency, if it is consistent.

Simplifications
Some simplifications may be made to the axiom schema of replacement to obtain different equivalent versions. Azriel Lévy showed that a version of replacement with parameters removed, i.e. the following schema, is equivalent to the original form. In particular the equivalence holds in the presence of the axioms of extensionality, pairing, union and powerset.

 * $$\forall A \, ( [ \forall x \, \exists ! y \, \phi(x, y, A) ]\ \Longrightarrow\ \exists B \, \forall y \, [y \in B \Leftrightarrow \exists x \in A \, \phi(x, y, A) ] )$$

Collection
The axiom schema of collection is closely related to and frequently confused with the axiom schema of replacement. Over the remainder of the ZF axioms, it is equivalent to the axiom schema of replacement. The axiom of collection is stronger than replacement in the absence of the power set axiom or its constructive counterpart of ZF but weaker in the framework of IZF, which lacks the law of excluded middle.

While replacement can be read to say that the image of a function is a set, collection speaks about images of relations and then merely says that some superclass of the relation's image is a set. In other words, the resulting set $$B$$ has no minimality requirement, i.e. this variant also lacks the uniqueness requirement on $$\phi$$. That is, the relation defined by $$\phi$$ is not required to be a function—some $$x\in A$$ may correspond to many $$y$$'s in $$B$$. In this case, the image set $$B$$ whose existence is asserted must contain at least one such $$y$$ for each $$x$$ in the original set, with no guarantee that it will contain only one.

Suppose that the free variables of $$\phi$$ are among $$w_1,\dotsc,w_n,x,y$$; but neither $$A$$ nor $$B$$ is free in $$\phi$$. Then the axiom schema is:

\forall w_1,\ldots,w_n \,[(\forall x\, \exists\, y \phi(x, y, w_1, \ldots, w_n)) \Rightarrow \forall A\, \exists B\, \forall x \in A\, \exists y \in B\, \phi(x, y, w_1, \ldots, w_n)] $$

The axiom schema is sometimes stated without prior restrictions (apart from $$B$$ not occurring free in $$\phi$$) on the predicate, $$\phi$$:

\forall w_1,\ldots,w_n \, \forall A\, \exists B\,\forall x \in A\, [ \exists y \phi(x, y, w_1, \ldots, w_n) \Rightarrow \exists y \in B\,\phi(x, y, w_1, \ldots, w_n)] $$

In this case, there may be elements $$x$$ in $$A$$ that are not associated to any other sets by $$\phi$$. However, the axiom schema as stated requires that, if an element $$x$$ of $$A$$ is associated with at least one set $$y$$, then the image set $$B$$ will contain at least one such $$y$$. The resulting axiom schema is also called the axiom schema of boundedness.

Separation
The axiom schema of separation, the other axiom schema in ZFC, is implied by the axiom schema of replacement and the axiom of empty set. Recall that the axiom schema of separation includes
 * $$\forall A\, \exists B\, \forall C\, (C \in B \Leftrightarrow [C \in A \land \theta(C)])$$

for each formula $$\theta$$ in the language of set theory in which $$B$$ is not free, i.e. $$\theta$$ that does not mention $$B$$.

The proof is as follows: Either $$A$$ contains some element $$a$$ validating $$\theta(a)$$, or it does not. In the latter case, taking the empty set for $$B$$ fulfills the relevant instance of the axiom schema of separation and one is done. Otherwise, choose such a fixed $$a$$ in $$A$$ that validates $$\theta(a)$$. Now define $$\phi(x, y):=(\theta(x)\land y=x)\lor(\neg\theta(x)\land y=a)$$ for use with replacement. Using function notation for this predicate $$\phi$$, it acts as the identity $$F_a(x)=x$$ wherever $$\theta(x)$$ is true and as the constant function $$F_a(x)=a$$ wherever $$\theta(x)$$ is false. By case analysis, the possible values $$y$$ are unique for any $$x$$, meaning $$F_a$$ indeed constitutes a class function. In turn, the image $$B := \{F_a(x) : x\in A\}$$ of $$A$$ under $$F_a$$, i.e. the class $$A\cap\{x : \theta(x)\}$$, is granted to be a set by the axiom of replacement. This $$B$$ precisely validates the axiom of separation.

This result shows that it is possible to axiomatize ZFC with a single infinite axiom schema. Because at least one such infinite schema is required (ZFC is not finitely axiomatizable), this shows that the axiom schema of replacement can stand as the only infinite axiom schema in ZFC if desired. Because the axiom schema of separation is not independent, it is sometimes omitted from contemporary statements of the Zermelo-Fraenkel axioms.

Separation is still important, however, for use in fragments of ZFC, because of historical considerations, and for comparison with alternative axiomatizations of set theory. A formulation of set theory that does not include the axiom of replacement will likely include some form of the axiom of separation, to ensure that its models contain a sufficiently rich collection of sets. In the study of models of set theory, it is sometimes useful to consider models of ZFC without replacement, such as the models $$V_\delta$$ in von Neumann's hierarchy.

The proof given above assumes the law of excluded middle for the proposition that $$A$$ is inhabited by a set validating $$\theta$$, and for any $$\theta(x)$$ when stipulating that the relation $$\phi$$ is functional. The axiom of separation is explicitly included in constructive set theory, or a bounded variant thereof.

Reflection
Lévy's reflection principle for ZFC is equivalent to the axiom of replacement, assuming the axiom of infinity. Lévy's principle is as follows:

 * For any $$x_1,\ldots,x_n$$ and any first-order formula $$\phi(x_1,\ldots,x_n)$$, there exists an $$\alpha$$ such that $$\phi(x_1,\ldots,x_n)\iff\phi^{V_\alpha}(x_1,\ldots,x_n)$$.

This is a schema that consists of countably many statements, one for each formula $$\phi$$. Here, $$\phi^M$$ means $$\phi$$ with all quantifiers bounded to $$M$$, i.e. $$\phi$$ but with every instance of $$\exists x$$ and $$\forall x$$ replaced with $$\exists(x\in V_\alpha)$$ and $$\forall(x\in V_\alpha)$$ respectively.

History
The axiom schema of replacement was not part of Ernst Zermelo's 1908 axiomatisation of set theory (Z). Some informal approximation to it existed in Cantor's unpublished works, and it appeared again informally in Mirimanoff (1917).

Its publication by Abraham Fraenkel in 1922 is what makes modern set theory Zermelo-Fraenkel set theory (ZFC). The axiom was independently discovered and announced by Thoralf Skolem later in the same year (and published in 1923). Zermelo himself incorporated Fraenkel's axiom in his revised system he published in 1930, which also included as a new axiom von Neumann's axiom of foundation. Although it is Skolem's first order version of the axiom list that we use today, he usually gets no credit since each individual axiom was developed earlier by either Zermelo or Fraenkel. The phrase “Zermelo-Fraenkel set theory” was first used in print by von Neumann in 1928.

Zermelo and Fraenkel had corresponded heavily in 1921; the axiom of replacement was a major topic of this exchange. Fraenkel initiated correspondence with Zermelo sometime in March 1921. However, his letters before the one dated 6 May 1921 are lost. Zermelo first admitted to a gap in his system in a reply to Fraenkel dated 9 May 1921. On 10 July 1921, Fraenkel completed and submitted for publication a paper (published in 1922) that described his axiom as allowing arbitrary replacements: "If M is a set and each element of M is replaced by [a set or an urelement] then M turns into a set again" (parenthetical completion and translation by Ebbinghaus). Fraenkel's 1922 publication thanked Zermelo for helpful arguments. Prior to this publication, Fraenkel publicly announced his new axiom at a meeting of the German Mathematical Society held in Jena on 22 September 1921. Zermelo was present at this meeting; in the discussion following Fraenkel's talk he accepted the axiom of replacement in general terms, but expressed reservations regarding its extent.

Thoralf Skolem made public his discovery of the gap in Zermelo's system (the same gap that Fraenkel had found) in a talk he gave on 6 July 1922 at the 5th Congress of Scandinavian Mathematicians, which was held in Helsinki; the proceedings of this congress were published in 1923. Skolem presented a resolution in terms of first-order definable replacements: "Let U be a definite proposition that holds for certain pairs (a, b) in the domain B; assume further, that for every a there exists at most one b such that U is true. Then, as a ranges over the elements of a set Ma, b ranges over all elements of a set Mb." In the same year, Fraenkel wrote a review of Skolem's paper, in which Fraenkel simply stated that Skolem's considerations correspond to his own.

Zermelo himself never accepted Skolem's formulation of the axiom schema of replacement. At one point he called Skolem's approach “set theory of the impoverished”. Zermelo envisaged a system that would allow for large cardinals. He also objected strongly to the philosophical implications of countable models of set theory, which followed from Skolem's first-order axiomatization. According to the biography of Zermelo by Heinz-Dieter Ebbinghaus, Zermelo's disapproval of Skolem's approach marked the end of Zermelo's influence on the developments of set theory and logic.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Axiom schema of replacement


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Independence Day (1996 film)

Independence Day (also promoted as ID4) is a 1996 American science fiction action film directed by Roland Emmerich, written by Emmerich and the film's producer Dean Devlin, and stars an ensemble cast that consists of Will Smith, Bill Pullman, Jeff Goldblum, Mary McDonnell, Judd Hirsch, Margaret Colin, Randy Quaid, Robert Loggia, Vivica A. Fox, James Rebhorn, and Harvey Fierstein. The film focuses on disparate groups of people who converge in the Nevada desert in the aftermath of a worldwide attack by a powerful extraterrestrial race. With the other people of the world, they launch a counterattack on July 4—Independence Day in the United States.

While promoting Stargate in Europe, Emmerich conceived the film while answering a question about his belief in the existence of alien life. Devlin and Emmerich decided to incorporate a large-scale attack having noticed that aliens in most invasion films travel long distances in outer space only to remain hidden when reaching Earth. Shooting began on July 28, 1995, in New York City, and the film was completed on October 8, 1995.

Considered a significant turning point in the history of the Hollywood blockbuster, Independence Day was at the forefront of the large-scale disaster film and sci-fi resurgence of the mid-late 1990s. It was released worldwide on July 3, 1996, but began showing on July 2 (the same day the film's story begins) in original release as a result of a high level of anticipation among moviegoers. The film received mixed reviews, with praise for the performances, musical score and visual effects, but criticism for its characters. It grossed over $817.4 million worldwide, becoming the highest-grossing film of 1996 and the second-highest-grossing film ever at the time, behind Jurassic Park (1993). The film won the Academy Award for Best Visual Effects and was nominated for the Academy Award for Best Sound.

The sequel, Independence Day: Resurgence, was released 20 years later on June 24, 2016, as part of a planned series of films.

Plot
On July 2, 1996, an extraterrestrial mothership enters Earth's orbit and deploys saucers (each 15 mi in diameter) over major cities worldwide, including New York City, Los Angeles and Washington, D.C.

U.S. Marine Captain Steven Hiller and his unit, the Black Knights fighter squadron out of MCAS El Toro, are called back from Independence Day leave to defend Los Angeles; his girlfriend, Jasmine Dubrow, decides to flee the city with her son, Dylan. Retired combat pilot Russell Casse, now an alcoholic single father and crop duster, sees this as vindication of the alien abduction he has been claiming for 10 years.

In New York City, technician David Levinson decodes a signal embedded within global satellite transmissions, realizing it is the aliens' countdown for a coordinated attack. With help from his ex-wife, White House Communications Director Constance Spano, David and his father Julius reach the Oval Office and alert President Thomas Whitmore.

Whitmore orders evacuations of the targeted cities in the U.S., but it is too late. Each saucer fires a beam, incinerating every targeted city, killing millions. Whitmore, the Levinsons, and a few others escape aboard Air Force One while Jasmine, Dylan, and their dog Boomer take shelter in a tunnel's inspection alcove, emerging once the destruction is over.

On July 3, counterattacks against the invaders are thwarted by the alien warships' force fields. Each saucer launches a swarm of shielded fighters which decimate the human fighter squadrons and military bases, including Captain Hiller's. Hiller lures an enemy fighter into the Grand Canyon before ejecting from his plane, blinding the fighter using his parachute and causing the alien to crash in the Mojave Desert. He subdues the downed alien and flags down a convoy of refugees, transporting the alien to Area 51, where Whitmore's group in Air Force One has landed.

Defense Secretary Albert Nimzicki reveals that a government faction has been involved in a UFO conspiracy since 1947 when one of the invaders' fighters crashed in Roswell. Area 51 houses the now-refurbished ship and three alien corpses recovered from the crash. As chief scientist Dr. Brackish Okun examines the alien captured by Steven, it awakens, telepathically invades Okun's mind and launches a psychic attack against Whitmore before being killed by Secret Service agents and military personnel. Whitmore reveals what he learned when they linked: the invaders' plan to annihilate Earth's inhabitants and harvest its natural resources, as they have already done to other planetary civilizations.

Whitmore reluctantly authorizes a trial nuclear attack against a saucer above Houston, but the ship is unharmed (with the city destroyed from the blast), and all subsequent nuclear attacks are aborted. Jasmine and Dylan commandeer a highway maintenance truck and rescue a handful of survivors, including the critically injured First Lady Marilyn Whitmore. Though Hiller rescues them and takes them to Area 51, Marilyn's injuries are too severe, and she dies after reuniting with her family.

On July 4, taking inspiration from his father, David writes a computer virus from his laptop to disrupt the aliens' shields' operating system, and devises a plan to upload it into the mothership from the refurbished alien fighter, which Hiller volunteers to pilot. The U.S. military contacts the world's remaining military forces and airborne squadrons through Morse code to organize a united counter-offensive. Lacking pilots, Whitmore and General William Grey enlist volunteers with flight experience, including Russell Casse, from the refugee camp at the base to fly the remaining jets at Area 51; Whitmore leads an attack on a saucer bearing down on the base, overseen by Grey.

Hiller marries Jasmine with David and Constance in attendance before leaving on the mission. Entering the mothership, they upload the virus and deploy a nuclear missile, destroying it and the aliens' invasion forces. With the shields deactivated, Whitmore's squadron engages a saucer and its fighters heading to Area 51 but exhausts their ammunition. As the saucer prepares to fire on the base, Russell sacrifices himself by crashing into the saucer's primary weapon before it fires, destroying the warship. Grey then orders notifications to the resistance groups worldwide of the spaceships' critical weakness and they destroy the others.

As humanity rejoices in their victory against the aliens, Hiller and Levinson reunite with their families.

Cast

 * Will Smith as Captain Steven Hiller, a Marine F/A-18 pilot squadron leader with the Black Knight squadron at MCAS El Toro and aspiring astronaut. The role was originally offered to Ethan Hawke but he turned it down as he thought the script was terrible. Devlin and Emmerich had always envisioned an African-American for the role, and specifically wanted Smith after seeing his performance in Six Degrees of Separation.
 * Bill Pullman as President Thomas J. Whitmore, a former fighter pilot and Gulf War veteran. To prepare for the role, Pullman read Bob Woodward's The Commanders and watched the documentary film The War Room.
 * Jeff Goldblum as David Levinson, an MIT-educated satellite engineer and technological expert.
 * Mary McDonnell as First Lady Marilyn Whitmore, the wife of Thomas Whitmore, who was fatally injured in a helicopter crash.
 * Judd Hirsch as Julius Levinson, David Levinson's father. The character was based on one of Dean Devlin's uncles.
 * Robert Loggia as General William Grey, USMC, the Commandant of the United States Marine Corps. Loggia modeled the character after World War II generals, particularly George S. Patton.
 * Randy Quaid as Russell Casse, an eccentric, alcoholic former fighter pilot and Vietnam War veteran. He insists that he was abducted by the aliens during work on aerial application ten years prior to the film's events, shortly after completing his military service.
 * Margaret Colin as Constance Spano, Whitmore's White House Communications Director and David Levinson's ex-wife.
 * Vivica A. Fox as Jasmine Dubrow, Steven Hiller's girlfriend and mother of Dylan Dubrow.
 * James Rebhorn as Albert Nimzicki, the Secretary of Defense and, as former CIA Director, is a member of a governmental faction who are aware of the aliens' existence due to the ship recovered at Roswell. Not well-liked, lying, arrogant, selfish, crooked, and often at odds with idealists such as Whitmore and Grey, Nimzicki embodies the stereotypical corrupt politician and his ambition is to be elected as president himself. Rebhorn described the character as being much like Oliver North. The character's eventual firing lampoons Joe Nimziki, MGM's head of advertising, who made life unpleasant for Devlin and Emmerich when studio executives forced recuts of Stargate.
 * Harvey Fierstein as Marty Gilbert, David Levinson's coworker at Compact Cable Television Company who is killed in the NYC attack.
 * Adam Baldwin as Major Mitchell, USAF, Area 51's commanding officer and thus a member of a governmental faction who are aware of the aliens' existence. During the interstellar war, he becomes a trusted ally to Thomas Whitmore's party.
 * Brent Spiner as Dr. Brackish Okun, the unkempt and highly excitable scientist in charge of research at Area 51. The character's appearance and verbal style are based upon those of visual effects supervisor Jeffrey A. Okun, with whom Emmerich had worked on Stargate.
 * James Duval as Miguel Casse, the oldest son of Russell Casse.
 * Bill Smitrovich as Lt. Colonel Watson, the commanding officer of the Black Knights.
 * Kiersten Warren as Tiffani, friend and co-worker of Jasmine who is killed in the LA attack.
 * Harry Connick Jr. as Marine Captain Jimmy Wilder, fellow fighter pilot and friend of Steven, killed in the Black Knight counterattack. Connick took over the role from Matthew Perry who was originally cast in the role.
 * Mae Whitman as Patricia Whitmore, the daughter of President Thomas J. Whitmore and First Lady Marilyn Whitmore.
 * Ross Bagley as Dylan Dubrow, Jasmine Dubrow's son and Steven Hiller's stepson.
 * Lisa Jakub as Alicia Casse, the daughter of Russell Casse.
 * Giuseppe Andrews as Troy Casse, the son of Russell Casse.
 * Frank Welker as special vocal effects.
 * Gary A. Hecker as alien vocal effects.

Development
The idea for the film came when Emmerich and Devlin were in Europe promoting their film Stargate. A reporter asked Emmerich why he made a film with content like Stargate if he did not believe in aliens. Emmerich stated he was still fascinated by the idea of an alien arrival, and further explained his response by asking the reporter to imagine what it would be like to wake up one morning and to discover 15-mile-wide spaceships were hovering over the world's largest cities. Emmerich then turned to Devlin and said, "I think I have an idea for our next film."

Emmerich and Devlin decided to expand on the idea by incorporating a large-scale attack, with Devlin saying he was bothered by the fact that "for the most part, in alien invasion movies, they come down to Earth and they're hidden in some back field …[o]r they arrive in little spores and inject themselves into the back of someone's head." Emmerich agreed by asking Devlin if arriving from across the galaxy, "would you hide on a farm or would you make a big entrance?" The two wrote the script during a month-long vacation in Mexico, and just one day after they sent it out for consideration, 20th Century Fox chairman Peter Chernin greenlit the screenplay. Pre-production began just three days later in February 1995. The U.S. military originally intended to provide personnel, vehicles, and costumes for the film; however, they backed out when the producers refused to remove the script's Area 51 references.

A then-record 3,000-plus special effects shots would ultimately be required for the film. The shoot utilized on-set, in-camera special effects more often than computer-generated effects in an effort to save money and get more authentic pyrotechnic results. Many of these shots were accomplished at Hughes Aircraft in Culver City, California, where the film's art department, motion control photography teams, pyrotechnics team, and model shop were headquartered. The production's model-making department built more than twice as many miniatures for the production than had ever been built for any film before by creating miniatures for buildings, city streets, aircraft, landmarks, and monuments. The crew also built miniatures for several of the spaceships featured in the film, including a 30 ft destroyer model and a version of the mother ship spanning 12 ft. City streets were recreated, then tilted upright beneath a high-speed camera mounted on a scaffolding filming downwards. An explosion would be ignited below the model, and flames would rise towards the camera, engulfing the tilted model and creating the rolling "wall of destruction" look seen in the film. A model of the White House was also created, covering 10 ft by 5 ft, and was used in forced-perspective shots before being destroyed in a similar fashion for its destruction scene. The detonation took a week to plan and required 40 explosive charges.

The film's aliens were designed by production designer Patrick Tatopoulos. The actual aliens in the film are diminutive and based on a design Tatopoulos drew when tasked by Emmerich to create an alien that was "both familiar and completely original". These creatures wear "bio-mechanical" suits that are based on another design Tatopoulos pitched to Emmerich. These suits were 8 ft tall, equipped with 25 tentacles, and purposely designed to show it could not sustain a person inside so it would not appear to be a "man in a suit".

Christopher Weaver, founder of video game publisher Bethesda Softworks consulted with the movie's production team, Centropolis Films, and provided scientific collaboration. Dean Devlin used Weaver as the basis for the film character David Levinson.

Filming
Principal photography began on July 28, 1995, in New York City. A second unit gathered plate shots and establishing shots of Manhattan, Washington, D.C., an RV community in Flagstaff, Arizona, and the Very Large Array on the Plains of San Agustin, New Mexico. The main crew also filmed in nearby Cliffside Park, New Jersey before moving to the former Kaiser Steel mill in Fontana, California to film the post-attack Los Angeles sequences. The production then moved to Wendover, Utah, and West Wendover, Nevada, where the deserts doubled for Imperial Valley, and the Wendover Airport doubled for the El Toro and Area 51 exteriors. It was here where Pullman filmed his pre-battle speech. Immediately before filming the scene, Devlin and Pullman decided to add "Today, we celebrate our Independence Day!" to the end of the speech. At the time, the production was nicknamed "ID4" because Warner Bros. owned the rights to the title because of a film from 1983 which is also called Independence Day. Devlin had hoped that if Fox executives noticed the addition in dailies, the impact of the new dialogue would help them to win the rights to the title. Pullman had stated in a 2020 interview that Fox had otherwise been aiming to use Doomsday for the film's release to match with other disaster films of the time, and Devlin and Emmerich had hoped the impact of this speech scene would help win Fox over to the Independence Day name. The right to use the title was eventually won two weeks later.

The production team moved to the Bonneville Salt Flats to film three scenes, then returned to California to film in various places around Los Angeles, including Hughes Aircraft where sets for the cable company and Area 51 interiors were constructed at a former aircraft plant. Sets for the latter included corridors containing windows that were covered with blue material. The filmmakers originally intended to use the chroma key technique to make it appear as if an activity was happening on the other side of the glass, but the composited images were not added to the final print because production designers decided the blue panels gave the sets a "clinical look". The attacker hangar set contained an attacker mockup 65 ft wide that took four months to build. The White House interior sets used had already been built for The American President and had previously been used for Nixon. Principal photography completed on October 8, 1995, after 72 days of filming.

The film initially depicted Russell Casse being rejected as a volunteer for the July 4 aerial counteroffensive because of his alcoholism. He then uses a stolen missile tied to his red biplane to carry out his suicide mission. According to Dean Devlin, test audiences responded well to the scene's irony and comedic value. However, the scene was re-shot to include Russell's acceptance as a volunteer, his crash course on flying modern fighter aircraft, and him flying an F/A-18 instead of the biplane. Devlin preferred the alteration because the viewer now witnesses Russell ultimately making the decision to sacrifice his life, and seeing the biplane keeping pace and flying amongst F/A-18s was "just not believable".

Music
The Grammy Award-winning score for the film was composed by David Arnold and recorded with an orchestra of 90, a choir of 46, "and every last ounce of stereotypical Americana he could muster for the occasion". The film's producer Dean Devlin commented that "you can leave it up to a Brit to write some of the most rousing and patriotic music in the history of American cinema." The soundtrack has received two official CD releases. RCA released a 50-minute album at the time of the film's release, then in 2010, La-La Land Records released a limited-edition, two-disc CD set that comprised the complete score plus 12 alternate cues. The premiere of Independence Day live took place at the Royal Albert Hall in September 2016, with the film's score performed live for a screening of the film. This celebrated the twentieth anniversary of the film's release, and the event also featured a pre-film talk by David Arnold.

Theatrical
While Independence Day was still in post-production, Fox began an expensive marketing campaign to help promote the film, beginning with the airing of a dramatic commercial during Super Bowl XXX, for which it paid $1.3 million. The film's subsequent success at the box office resulted in a trend of using Super Bowl air time to begin the advertising campaigns for potential blockbusters.

Fox's Licensing and Merchandising division also entered into co-promotional deals with Apple Inc. The co-marketing project was dubbed "The Power to Save the World" campaign, in which the company used footage of David using his PowerBook 5300 laptop in their print and television advertisements. Trendmasters entered a merchandising deal with the film's producers to create a line of tie-in toys. In exchange for product placement, Fox also entered into co-promotional deals with Molson Coors Brewing Company and Coca-Cola.

The film was marketed with several taglines, including: "We've always believed we weren't alone. On July 4, we'll wish we were", "Earth. Take a good look. It could be your last", and "Don't make plans for August". The weekend before the film's release, the Fox Network aired a half-hour special on the film, the first third of which was a spoof news report on the events that happen in the film. Roger Ebert attributed most of the film's early success to its teaser trailers and marketing campaigns, acknowledging them as "truly brilliant".

The film had its official premiere held at Los Angeles' now-defunct Mann Plaza Theater on June 25, 1996. It was then screened privately at the White House for President Bill Clinton and his family before receiving a nationwide release in the United States on July 2, 1996, a day earlier than its previously scheduled opening.

Censorship
In Lebanon, certain Jewish- and Israel-related content in the film was censored. One cut scene involved Judd Hirsch's character donning a kippah, and leading soldiers and White House officials in a Jewish prayer. Other removed footage showed Israeli and Arab troops working together in preparation for countering the alien invasion. The Lebanese Shi'a Islamist militant group Hezbollah called for Muslims to boycott the film, describing it as "propaganda for the so-called genius of the Jews and their concern for humanity." In response, Jewish actor Jeff Goldblum said: "I think Hezbollah has missed the point. The film is not about American Jews saving the world; it's about teamwork among people of different religions and nationalities to defeat a common enemy."

Home media
After a six-week, $30 million marketing campaign, Independence Day was released on a THX certified VHS on November 22, 1996. A LaserDisc release came out at roughly the same time, which included audio commentary, theatrical trailers, deleted scenes, and a bundled soundtrack CD. The film sold 22 million copies in North America, becoming the best selling live-action video.

The film became available on DVD on June 27, 2000, and has since been re-released in several different versions of this format with varying supplemental material, including one instance where it was packaged with a lenticular cover. A special edition of the film was included on the DVD as well, which features nine minutes of additional footage not seen in the original theatrical release. A single-disc DVD version of the film was released alongside Cast Away on May 21, 2002. Independence Day became available on Blu-ray in the United Kingdom on December 24, 2007, and in North America on March 11, 2008 and in Australia on March 5, 2008. The initial single-disc releases only feature the theatrical cut and a few extras, as per the single-disc DVDs. For its 2016 twentieth anniversary, the film was re-released on two-disc Blu-ray and DVD, 4K Ultra HD Blu-ray, and Digital HD. The 20th-anniversary editions feature both the theatrical and extended versions, all the extras of the previous 2-disc DVDs and more.

Television broadcast
Independence Day was originally scheduled to air on Fox on September 16, 2001, but was cancelled following the September 11 attacks. Fox replaced Independence Day with a repeat airing of There's Something About Mary.

Re-release
The film had both its twentieth anniversary and premiere at a special live-orchestral screening performance at the Royal Albert Hall on September 22, 2016. The Royal Philharmonic Orchestra, conducted by the original orchestrator Nicholas Dodd, performed the score live during the film, and the film's composer, David Arnold, was a presenter at the event.

Box office
Independence Day was the highest-grossing film of 1996, surpassing both Twister and Mission: Impossible. The film had its preview screenings on July 2, 1996, grossing $11.1 million from 2,433 theaters. At that point, it had the biggest pre-opening of any film, breaking the six-year record held by Die Hard 2. The next day on July 3, the film officially opened to the public with $17.4 million. During its second day of release, it earned $17.3 million, which made it the highest Thursday gross, holding this record for six years until it was taken by Star Wars: Episode II – Attack of the Clones in 2002. This was also the highest non-sequel Thursday gross, which would last until the opening of Transformers in 2007. Independence Day earned $104.3 million in its opening week, including $96.1 million during its five-day holiday opening, and $50.2 million during its opening weekend. The film stayed in the number-one spot for three consecutive weeks before being displaced by A Time to Kill. Moreover, it beat Terminator 2: Judgment Day's record for largest five-day Wednesday gross of any film, as well as the biggest July opening weekend. The combined total for the five-day Wednesday opening increased to $190 million, dethroning the $158.6 million record held by Toy Story. In addition, the film had the second-highest opening weekend of any movie, behind Batman Forever. All three figures broke records set by Jurassic Park three years earlier, whose successor, The Lost World: Jurassic Park, claimed all three records when it was released in 1997. That same year, Men in Black surpassed Independence Day for highest July opening weekend and largest three-day Fourth of July opening weekend. Despite this, the film would continue to hold the record for having the highest five-day Fourth of July Wednesday opening until Men in Black II in 2002.

Independence Day earned over $150 million in 12 days, becoming the quickest film to do so. In 21 days, it became the fastest film to approach the $200 million mark. The film would hold this record for three years until it was surpassed by Star Wars: Episode I – The Phantom Menace in 1999. By the end of July 1996, Independence Day had lost 38% of its audience, but it was able to top Ghostbusters, Aladdin, Mrs. Doubtfire and Ghost, becoming the fourteenth-highest domestic grossing film of all time. It reached $230 million within the first month of release, and on August 9, crossed the $250 million mark. Halfway through the month, it became the eighth-highest domestic grosser, beating Jaws.

Independence Day grossed $306,169,268 in the United States and Canada and $511,231,623 in other territories during its theatrical run. The combined worldwide total of $817,400,891 surpassed The Lion King, second only to the worldwide earnings of Jurassic Park as the highest of all time. For over 20 years, the film would hold the record for being the highest-grossing film starring Will Smith until 2019 when it was surpassed by the live-action version of Aladdin. The domestic record was beaten by Suicide Squad three years earlier in 2016. In the UK, the film grossed £7,005,905 in its opening weekend (including £939,022 from previews), surpassing Jurassic Park's record of £4.9 million. The film grossed a record $10.5 million in its opening weekend in Germany and also beat the opening record in France. Box Office Mojo estimates that the film sold over 69.26 million tickets in the US and Canada. Hoping to capitalize on the film's success, several studios released large-scale disaster films, and the already rising interest in science fiction-related media was further increased by the film's popularity.

A month after the film's release, jewelry designers and marketing consultants reported an increased interest in dolphin-themed jewelry, as the character Jasmine (Vivica A. Fox) wears dolphin earrings, and is presented with a wedding ring featuring a gold dolphin.

Critical response
Review aggregator Rotten Tomatoes reports that 68% of 81 surveyed critics gave the film a positive review; the average rating is 6.6/10. The site's critical consensus reads, "The plot is thin and so is character development, but as a thrilling, spectacle-filled summer movie, Independence Day delivers." On Metacritic, the film has a score of 59 out of 100 based on 19 critics, indicating "mixed or average reviews". Audiences polled by CinemaScore gave the film an average grade of "A" on an A+ to F scale.

Critics wrote that the film has "cardboard" and "stereotypical" characters,   and weak dialogue. However, the shot of the White House's destruction was declared a milestone in visual effects and one of the most memorable scenes of the 1990s. In a 2010 poll, readers of Entertainment Weekly rated it the second-greatest summer film of the previous 20 years, ranking only behind Jurassic Park.

Mick LaSalle of the San Francisco Chronicle gave the film his highest rating, declaring it the "apotheosis" of comic book space adventure movies. Lisa Schwarzbaum of Entertainment Weekly gave it a B+ for living up to its massive hype, adding "charm is the foremost of this epic's contemporary characteristics. The script is witty, knowing, cool." Eight years later, Entertainment Weekly rated the film as one of the best disaster films of all time. Kenneth Turan of the Los Angeles Times felt that the film did an "excellent job conveying the boggling immensity of [the] extraterrestrial vehicles […] and panic in the streets" and the scenes of the alien attack were "disturbing, unsettling and completely convincing".

The film's nationalistic overtones were widely criticized by reviewers outside the U.S. Movie Review UK described the film as "a mish-mash of elements from a wide variety of alien invasion movies and gung-ho American jingoism." The speech during which Whitmore states that victory in the coming war would see the entire world henceforth describe July 4 as its Independence Day, was described in a BBC review as "the most jaw-droppingly pompous soliloquy ever delivered in a mainstream Hollywood movie." In 2003, readers of Empire voted that scene as the "Cheesiest Movie Moment of All-Time". Empire critic Kim Newman had given the film a five-star rating in the magazine's original review.

Several critics were disappointed by the special effects. Newsweek's David Ansen claimed they were no better than those seen nineteen years earlier in Star Wars. Todd McCarthy of Variety felt the production's budget-conscious approach resulted in "cheesy" shots, lacking the quality of effects in films by James Cameron and Steven Spielberg. Roger Ebert noted a lack of imagination in the spaceship and creature designs. Gene Siskel expressed the same sentiments in his At the Movies review.

American Film Institute lists
 * AFI's 100 Years...100 Thrills – Nominated
 * AFI's 10 Top 10 – Nominated Science Fiction Film

Legacy
Disaster elements portrayed in Twister and Independence Day (both in 1996) represented a significant turning point for Hollywood blockbuster films. With advancements in CGI special effects, events depicting mass destruction became commonplace in films that soon followed, such as Dante's Peak and Volcano (both in 1997), as well as Deep Impact and Armageddon (both in 1998). The trend resumed from the mid-2000s to 2010s, evident in three of Emmerich's films titled The Day After Tomorrow (2004), 2012 (2009), and White House Down (2013), as well as other blockbusters like Transformers (2007) and The Avengers (2012).

Books
Author Stephen Molstad wrote a tie-in novel to help promote the film shortly before its release. The novel goes into further detail on the characters, situations, and overall concepts not explored in the film. The novel presents the film's finale as originally scripted, with the character played by Randy Quaid stealing a missile and roping it to his cropduster biplane.

Following the film's success, a prequel novel entitled Independence Day: Silent Zone was written by Molstad in February 1998. The novel is set in the late 1960s and early 1970s, and details the early career of Dr. Brackish Okun.

Molstad wrote a third novel, Independence Day: War in the Desert in July 1999. Set in Saudi Arabia on July 3, it centers around the two Royal Air Force officers seen receiving the Morse code message in the film. A Marvel comic book was also written based on the first two novelizations.

Radio
On August 4, 1996, BBC Radio 1 broadcast the one-hour play Independence Day UK, written, produced, and directed by Dirk Maggs, a spin-off depicting the alien invasion from a British perspective. None of the original cast was present. Dean Devlin gave Maggs permission to produce an original version, on the condition that he did not reveal certain details of the movie's plot, and that the British were not depicted as saving the day. Independence Day UK was set up to be similar to the 1938 radio broadcast of The War of the Worlds—the first 20 minutes were live.

Multimedia
In 1996 a "behind-the-scenes" multimedia CD-ROM titled Inside Independence Day was released for Microsoft Windows and Macintosh; it includes storyboards for the film, sketches, movie clips, and a preview of the Independence Day video game.

Video games
An Independence Day video game was released in February 1997 for the PlayStation, Sega Saturn, and PC, each version receiving mostly tepid reviews. The multi-view shooter game contains various missions to perform, with the ultimate goal of destroying the aliens' primary weapon. A pinball machine themed to the film was released by Sega in June 1996. Plus, a wireless mobile version was released in 2005.

A video game entitled ID4 Online (or Independence Day Online) was released by Mythic Entertainment.

Toys
Trendmasters released a toy line for the film in 1996. Each action figure, vehicle or playset came with a $3 1/2$ inch floppy disk that contained an interactive computer game.

Franchise
In June 2011, Devlin confirmed that he and Emmerich had written a treatment for two sequels to form a trilogy; both expressed the desire for Will Smith to return. In October 2011, however, discussions over Smith returning were halted, due to Fox's refusal to provide the $50 million salary demanded by Smith for the two sequels. Emmerich, however, made assurances that the films would be shot back-to-back, regardless of Smith's involvement.

In March 2013, Emmerich stated that the titles of the new films would be ID: Forever – Part I and ID: Forever – Part II. In November 2014, the sequel was given the green light by 20th Century Fox, with a release date of June 24, 2016. This would be a stand-alone sequel, that would not split into two parts as originally planned, with filming beginning in May 2015 and casting being done after the studio locked down Emmerich as the director of the film. In December 2014, Devlin confirmed that Emmerich would indeed be directing the sequel. On June 22, 2015, Emmerich announced the official title, Independence Day: Resurgence.

With respect to Smith's decision not to return to film a sequel, Emmerich told Screen Crush that: "In the very beginning, I wanted to work with him and he was excited to be in it but then after a while he was tired of sequels, and he did another science fiction film, which was his father-son story After Earth, so he opted out."

Independence Day: Resurgence was released on June 24, 2016. The sequel, unlike the original, was both a critical and commercial failure, making further sequels unlikely. Furthermore, in March 2018, LRM Online reported that, after having met producer Dean Devlin at WonderCon and asking about the status of Independence Day 3, Devlin told them "I don't know. I don't know. Currently, I personally have no plans of doing another one." One year later, Emmerich stated that once The Walt Disney Company purchased Fox he thought the chances of a third movie were over, but still had hopes that the project could happen given Disney's preference for franchise films.

title: Independence Day (1996 film)


text:
Armageddon (1998 film)

Armageddon is a 1998 American science fiction disaster film produced and directed by Michael Bay, produced by Jerry Bruckheimer, and released by Touchstone Pictures. The film follows a group of blue-collar deep-core drillers sent by NASA to stop a gigantic asteroid on a collision course with Earth. It stars an ensemble cast consisting of Bruce Willis with Billy Bob Thornton, Liv Tyler, Ben Affleck, Will Patton, Peter Stormare, Keith David, and Steve Buscemi.

The film was a commercial success, grossing $553.7 million worldwide against a $140 million budget and becoming the highest-grossing film of 1998, and the highest-grossing film to be released by Touchstone Pictures. The film received mixed reviews from critics.

Plot
A massive meteor shower destroys the orbiting Space Shuttle Atlantis, before entering the atmosphere and bombarding New York City, Boston, Philadelphia, Moncton, Halifax, and Newfoundland. The meteors were pushed out of the asteroid belt by a collision from a rogue comet, which also dislodged a massive asteroid the size of Texas, and NASA learns that the asteroid will impact Earth in 18 days, potentially wiping out all life on Earth. NASA devises a plan to have a deep hole drilled into the asteroid, into which they will insert and detonate a nuclear bomb to destroy the asteroid.

They recruit Harry Stamper, a third-generation oil driller and owner of his own oil drilling company. Harry agrees to help, but on the condition that he bring in his own team to do the drilling. He picks his best employees for the job: Chick Chapel, his best friend and right-hand man; geologists Rockhound and Oscar Choice; and drillers Bear Curlene, Freddie Noonan, Max Lennert, and A.J. Frost (who has been dating Harry's daughter Grace despite Harry's objections). Over twelve days, they are trained to become astronauts with astronaut Willie Sharp, who will pilot Freedom — one of the two shuttles to fly to the asteroid, the other being the Independence. Before leaving, Chick apologizes to his ex-wife for wronging her and sees his son, who is unaware of his parentage. Grace accepts A.J.'s marriage proposal, much to Harry's reluctant dismay; she later has her father promise to return home safe with her fiancé.

Following the destruction of Shanghai by another meteor strike, word of the massive asteroid becomes public to the world. Both shuttles take off without incident and dock with the Russian space station Mir to take on fuel. However, a leaky pipeline ignites the fuel pod on fire. A.J. and Roscosmos Cosmonaut Lev Andropov narrowly manage to board Independence before the space station is destroyed.

Approaching the asteroid, Independence is damaged by debris and crashes, killing all on board except Lev, Bear, and A.J. They embark in the shuttle's Armadillo to find the Freedom crew, which lands 26 miles from its intended landing site. When the drilling goes slower than predicted, Sharp reports to Mission Control that it is unlikely the team will reach the depth necessary to destroy the asteroid before "Zero Barrier", the point after which detonating the rock will not save Earth. The President of the United States decides to remotely detonate the bomb from Earth immediately, which will cause total mission failure. Sharp and Harry have a vicious argument, but agree to defuse the bomb and work together after Harry promises Sharp that he will accomplish the mission. They make progress on drilling, but a missed gas pocket causes the Armadillo and Max to be blown into space. Just as Harry, NASA, and the world believe the mission to be a failure, while another meteor destroys Paris, A.J. and the others arrive in the second Armadillo.

A.J. succeeds in drilling the hole to the required depth, but a rock storm kills Gruber and damages the remote detonator, forcing someone to stay behind and manually detonate the bomb. They draw straws; the responsibility falls upon A.J.. Harry takes him down to the asteroid's surface, only to disconnect A.J.'s air hose and force him into the shuttle's air lock. Harry then tells A.J. that he is the son Harry never had, and he would be proud to have him marry Grace. Using the Armadillo, Harry tearfully gives Grace his blessing to marry A.J., and Grace says that she is proud to be his daughter.

After some difficulty, Freedom takes off, but then a second blowout causes Harry to lose his grip on the detonator. Just before Zero Barrier, he manages to detonate the bomb and saves the planet. The astronauts land on Earth safely. A.J. and Grace are reunited and Chick reconciles with his ex-wife and estranged son. Later, A.J. and Grace are married, with the portraits of Harry and the others lost on the mission present in memoriam.

Development
According to Bruce Joel Rubin, writer of Deep Impact, a production president at Disney took notes on everything the writer said during lunch about his script and initiated Armageddon as a counter film at Disney. Nine writers worked on the script, five of whom are credited. In addition to Robert Roy Pool, Jonathan Hensleigh, Tony Gilroy, Shane Salerno and J. J. Abrams, the writers involved included Paul Attanasio, Ann Biderman, Scott Rosenberg and Robert Towne. Originally, it was Hensleigh's script, based on Pool's original, that had been given the green-light by Touchstone. Then-producer, Jerry Bruckheimer, hired the succession of scribes for rewrites and polishes.

Bruce Willis was cast in the film as part of a three-picture deal he cut with the studio to compensate them for the dissolution of 1997's Broadway Brawler. He received a significant pay cut for the picture as part of the deal. Sean Connery was originally considered for the role of Stamper, but Bay decided to cast a younger actor in the role after meeting oil drillers.

Filming
Principal photography for Armageddon began in August 27, 1997 and ended on January 29, 1998. Filming occurred at Culver Studios in Culver City, California. In May 1998, Walt Disney Studios chairman Joe Roth expanded the film's budget by $3 million to include additional special effects scenes by Dream Quest Images showing an asteroid impacting Paris. This additional footage, incorporated two months prior to the film's release, was specifically added for the television advertising campaign to visually differentiate the film from Deep Impact which was released a few months before. At a budget of $140 million, it was Buena Vista's most expensive film at the time.

Marketing
Prior to Armageddon's release, the film was advertised in Super Bowl XXXII at a cost of $2.6 million.

Home media
Despite a mixed critical reception, The Criterion Collection—a specialist film distributor of primarily arthouse films that markets what it considers to be "important classic and contemporary films" and "cinema at its finest"—released the 'directors cut' of the film to DVD and Laserdisc. In an essay supporting the selection of Armageddon, film scholar Jeanine Basinger, who taught Michael Bay at Wesleyan University, states that the film is "a work of art by a cutting-edge artist who is a master of movement, light, color, and shape—and also of chaos, razzle-dazzle, and explosion". She sees it as a celebration of working men: "This film makes these ordinary men noble, lifting their efforts up into an epic event." Further, she states that in the first few moments of the film all the main characters are well established, saying, "If that isn't screenwriting, I don't know what is".

The film was also released on VHS and DVD by Touchstone Home Video on November 13, 1998, and would surpass Pretty Woman to become Buena Vista Home Entertainment's best-selling live-action title. Armageddon then premiered on both VHS and DVD formats on February 1, 1999, in the UK. It was the country's best-selling DVD release, selling over 100,000 copies. However, this record would be surpassed by The Matrix later that year. The film was released on a standard edition Blu-ray in 2010 with only a few special features.

Television airing
By April 2002, ABC airings of Armageddon had already received modifications due to the September 11 attacks that occurred seven months prior. The scene where the World Trade Center was hit by meteors and caught on fire was edited out because of its similarity to the attacks.

Following the 2003 Columbia disaster, some screen captures from the opening scene where Atlantis is destroyed were passed off as satellite images of the disaster in a hoax. Additionally, the American cable network FX, which had intended to broadcast Armageddon that evening, removed the film from its schedule and aired Aliens in its place.

Box office
Armageddon was released on July 1, 1998 in 3,127 theaters in the United States and Canada. It ranked first at the box office ahead of Dr. Dolittle with an opening weekend gross of $36 million, combined with $54.2 million from its first five days. Upon opening, the film had the third-highest Fourth of July opening weekend at the time, behind Men in Black and Independence Day. The film was dethroned by Lethal Weapon 4 in its second weekend, although it collected a total of $23.5 million. In late July 1998, it surpassed its rival Deep Impact to become the highest-grossing domestic release of the year. The film grossed $201.6 million in the United States and Canada and $352.1 million in other territories for a worldwide total of $553.7 million. It was the highest-grossing film of 1998 worldwide and the second-highest-grossing film of that year in the United States, finishing just behind Saving Private Ryan.

Critical response
Armageddon  received mostly mixed reviews from film critics, many of whom took issue with "the furious pace of its editing". On the review aggregator website Rotten Tomatoes, the film has a 43% approval rating based on 176 reviews, with an average rating of 5.3/10. The critical consensus states, "Lovely to look at but about as intelligent as the asteroid that serves as the movie's antagonist, Armageddon slickly sums up the cinematic legacies of producer Jerry Bruckheimer and director Michael Bay." Metacritic gave the film a weighted average score of 42 out of 100, based on 23 critics, indicating "mixed or average reviews". Audiences polled by CinemaScore gave the film an average grade of "A−" on an A+ to F scale.

The film is on the list of Roger Ebert's most hated films. In his original review, Ebert stated, "The movie is an assault on the eyes, the ears, the brain, common sense and the human desire to be entertained". On Siskel and Ebert, Ebert gave it a Thumbs Down. However, his co-host Gene Siskel gave it a Thumbs Up, commenting on the noise and intensity of the film, but also stating that he found the film to be amusing. Ebert went on to name Armageddon as the worst film of 1998 (though he was originally considering Spice World). Todd McCarthy of Variety also gave the film a negative review, noting Michael Bay's rapid cutting style: "Much of the confusion, as well as the lack of dramatic rhythm or character development, results directly from Bay's cutting style, which resembles a machine gun stuck in the firing position for 21⁄2 hours." In April 2013, in a Miami Herald interview to promote Pain & Gain, Bay was quoted as having said:"…We had to do the whole movie in 16 weeks. It was a massive undertaking. That was not fair to the movie. I would redo the entire third act if I could. But the studio literally took the movie away from us. It was terrible. My visual effects supervisor had a nervous breakdown, so I had to be in charge of that. I called James Cameron and asked 'What do you do when you're doing all the effects yourself?' But the movie did fine."Some time after the article was published, Bay changed his stance, claiming that his apology only related to the editing of the film, not the whole film, and accused the writer of the article for taking his words out of context. The author of the article, Miami Herald writer Rene Rodriguez, claimed: "NBC asked me for a response, and I played them the tape. I didn't misquote anyone. All the sites that picked up the story did."

Scientific accuracy
In an interview with Entertainment Weekly, Bay admitted that the film's central premise "that NASA could actually do something in a situation like this" was unrealistic. Additionally, the largest known potentially hazardous asteroid (PHA) is (53319) 1999 JM8, which is only 7 km in diameter, while the asteroid in the movie is described as being "the size of Texas". Near the end of the credits, there is a disclaimer stating, "The National Aeronautics and Space Administration's cooperation and assistance does not reflect an endorsement of the contents of the film or the treatment of the characters depicted therein." Astronomers would subsequently note that Deep Impact was more scientifically accurate.

The infeasibility of the H-bomb approach was published by four postgraduate physics students in 2011 and then reported by The Daily Telegraph in 2012:

"A mathematical analysis of the situation found that for Willis's approach to be effective, he would need to be in possession of an H-bomb a billion times stronger than the Soviet Union's 'Big Ivan', the biggest ever detonated on Earth. Using estimates of the asteroid's size, density, speed and distance from Earth based on information in the film, the postgraduate students from Leicester University found that to split the asteroid in two, with both pieces clearing Earth, would require 800 trillion terajoules of energy. In contrast, the total energy output of 'Big Ivan', which was tested by the Soviet Union in 1961, was only 418,000 terajoules."

In the commentary track, Ben Affleck says he "asked Michael why it was easier to train oil drillers to become astronauts than it was to train astronauts to become oil drillers, and he told me to shut the fuck up, so that was the end of that talk."

Neil deGrasse Tyson said on the October 2, 2023 episode of The Late Show with Stephen Colbert that, until the release of the 2022 film Moonfall, Armageddon was the movie which violated more laws of physics per minute than any other movie ever.

Merchandising
Revell and Monogram released two model kits inspired by the film's spacecraft and the Armadillos, in 1998. The first one, "Space Shuttle with Armadillo drilling unit", included an X-71, a small, rough Armadillo and a pedestal. The second one, "Russian Space Center", included the Mir, with the docking adapter seen in the film, and another pedestal.

In 2011, Fantastic Plastic released another X-71 kit, the "X-71 Super Shuttle", the goal of which was to be more accurate than the Revell/Monogram kit.

Theme park attraction
Armageddon – Les Effets Speciaux was an attraction based on Armageddon at Walt Disney Studios Park located at Disneyland Paris. The attraction simulated the scene in the movie in which the Russian Space Station is destroyed. Michael Clarke Duncan ("Bear" in the film) was featured in the pre-show.

title: Armageddon (1998 film)


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Prince Maximilian of Baden

Maximilian, Margrave of Baden (Maximilian Alexander Friedrich Wilhelm; 10 July 1867 – 6 November 1929), also known as Max von Baden, was a German prince, general, and politician. He was heir presumptive to the throne of the Grand Duchy of Baden, and in October and November 1918 briefly served as the last chancellor of the German Empire and minister-president of Prussia. He sued for peace on Germany's behalf at the end of World War I based on U.S. President Woodrow Wilson's Fourteen Points and took steps towards transforming the government into a parliamentary system. As the German Revolution of 1918–1919 spread, he handed over the office of chancellor to SPD Chairman Friedrich Ebert and unilaterally proclaimed the abdication of Emperor Wilhelm II. Both events took place on 9 November 1918, marking the beginning of the Weimar Republic.

Early life

Born in Baden-Baden on 10 July 1867, Maximilian was a member of the House of Baden, the son of Prince Wilhelm Max (1829–1897), third son of Grand Duke Leopold (1790–1852) and Princess Maria Maximilianovna of Leuchtenberg (1841–1914), a granddaughter of Eugène de Beauharnais. He was named after his maternal grandfather, Maximilian de Beauharnais, and bore a resemblance to his cousin, Emperor Napoleon III.

Max received a humanistic education at a Gymnasium secondary school and studied law and cameralism at the Leipzig University. Upon the order of Queen Victoria, Prince Max was brought to Darmstadt in the Grand Duchy of Hesse and by Rhine as a suitor for Victoria's granddaughter, Alix of Hesse-Darmstadt. Alix was the daughter of Victoria's late daughter, Princess Alice, and Louis IV, Grand Duke of Hesse. Alix quickly rejected Prince Max, as she was in love with Nicholas II, the future Tsar of Russia. Max von Baden was homosexual and even listed on an according list of the Berlin criminal police as a young officer, however in 1900 he decided for dynastic reasons to marry Princess Marie Louise of Hanover and Cumberland. So did the future King Gustaf V of Sweden who married Max's cousin Victoria of Baden.

Early military and political career
After finishing his studies, he trained as an officer of the Prussian Army. Following the death of his uncle Grand Duke Frederick I of Baden in 1907, he became heir to the grand-ducal throne of his cousin Frederick II, whose marriage remained childless. He also became president of the Erste Badische Kammer (the upper house of the parliament of Baden). In 1911, Max applied for a military discharge with the rank of a Generalmajor (Major general).

World War I
Upon the outbreak of World War I in 1914, he served as a general staff officer at the XIV Corps of the German Army as the representative of the Grand Duke (XIV Corps included the troops from Baden). Shortly afterwards, however, he retired from his position (General der Kavallerie à la suite) as he was dissatisfied with his role in the military and was suffering from ill health.

In October 1914, he became honorary president of the Baden section of the German Red Cross, thus beginning his work for prisoners-of-war inside and outside Germany in which he made use of his family connections to the Russian and Swedish courts as well as his connections to Switzerland. In 1916, he became honorary president of the German-American support union for prisoners of war within the YMCA world alliance.

Due to his liberal stance he came into conflict with the policies of the Oberste Heeresleitung (OHL – Supreme Army Command) supreme command under Paul von Hindenburg and Erich Ludendorff. He openly spoke against the resumption of the unrestricted submarine warfare in 1917, which provoked the declaration of war by the United States Congress on 6 April.

His activity in the interests of prisoners of war, as well as his tolerant, easy-going character gave him a reputation as an urbane personality who kept his distance from the extremes of nationalism and official war enthusiasm in evidence elsewhere at the time. Since he was almost unknown to the public, it was mainly due to Kurt Hahn, who served from spring 1917 in the military office of the Foreign Ministry, that he was later considered for the position of chancellor. Hahn maintained close links with Secretary of State Wilhelm Solf and several Reichstag deputies like Eduard David (SPD) and Conrad Haußmann (FVP). David pushed for Max to be appointed Chancellor in July 1917, after the fall of Chancellor Bethmann Hollweg. Max then put himself forward for the position in early September 1918, pointing out his links to the social democrats, but Emperor Wilhelm II turned him down.

Appointment
After the Oberste Heeresleitung (OHL) told the government in late September 1918 that the German front was about to collapse and asked for immediate negotiation of an armistice, the cabinet of Chancellor Georg von Hertling resigned on 30 September 1918. Hertling, after consulting Vice-Chancellor Friedrich von Payer (FVP), suggested Prince Max of Baden as his successor to the emperor. However, it took the additional support of Haußmann, Oberst and Ludendorff himself to have Wilhelm II appoint Max as Chancellor of Germany and Minister President of Prussia.

Max was to head a new government, based on the majority parties of the Reichstag (SPD, Centre Party and FVP). When Max arrived in Berlin on 1 October, he had no idea that he would be asked to approach the Allies about an armistice. Horrified, Max fought against the plan. Moreover, he also admitted openly that he was no politician, and that he did not think additional steps towards "parliamentarisation" and democratisation feasible, as long as the war continued. Consequently, he did not favour a liberal reform of the constitution. However, Emperor Wilhelm II convinced him to take the post, and appointed him on 3 October 1918. The message asking for an armistice went out only on 4 October, not as originally planned on 1 October, hopefully to be accepted by US President Woodrow Wilson.

In office
Although Max had serious reservations about the conditions under which the OHL was willing to conduct negotiations and tried to interpret Wilson's Fourteen Points in a way most favourable to the German position, he accepted the charge. He appointed a government that for the first time included representatives of the largest party in the Reichstag, the Social Democratic Party of Germany, as state secretaries (equivalent to ministers in other monarchies): Philipp Scheidemann and Gustav Bauer. This was following up on an idea of Ludendorff's and former Foreign Secretary Paul von Hintze's (as the representative of the Hertling cabinet) who had agreed on 29 September that the request for an armistice must not come from the old regime, but from one based on the majority parties. The official reason for appointing a government based on a parliamentary majority was to make it harder for the American president to refuse a peace offer. The need to convince Wilson was also the driving factor behind the move towards "parliamentarisation" that was to make the Chancellor and his government answerable to the Reichstag, as they had not been under the Empire so far. Ludendorff, however, was more interested in shifting the blame for the lost war to the politicians and to the Reichstag parties.

The Allies were cautious, distrusting Max as a member of a ruling family of Germany. These doubts were intensified by the publication of a personal letter Max had written to Prince Alexander zu Hohenlohe-Schillingsfürst in early 1918, in which he had expressed criticism of "parliamentarisation" and his opposition to the Friedensresolution of the Reichstag of July 1917, when a majority had demanded a negotiated peace rather than a peace by victory. President Wilson reacted with reserve to the German initiative and took his time to agree to the request for an armistice, sending three diplomatic notes between 8 October and 23 October 1918. When Ludendorff changed his mind about the armistice and suddenly advocated continued fighting, Max opposed him in a cabinet meeting on 17 October 1918. On 24 October, Ludendorff issued an army order that called Wilson's third note "unacceptable" and called on the troops to fight on. On 25 October, Hindenburg and Ludendorff then ignored explicit instructions by the Chancellor and travelled to Berlin. Max asked for Ludendorff to be dismissed; Wilhelm II agreed. On 26 October, the emperor told Ludendorff that he had lost his trust. Ludendorff offered his resignation and Wilhelm II accepted.

While trying to move towards an armistice, Max, advised closely by Hahn (who also wrote his speeches), Haußmann and Walter Simons, worked with the representatives of the majority parties in his cabinet (Scheidemann and Bauer for the SPD, Matthias Erzberger, and  for the Centre Party, Payer and, after 14 October, Haußmann for the FVP). Although some of the initiatives were a result of the notes sent by Wilson, they were also in line with the parties' manifestos: making the Chancellor, his government and the Prussian Minister of War answerable to parliament (Reichstag and Preußischer Landtag), introducing a more democratic voting system in the place of the Dreiklassenwahlrecht (Three-class franchise) in Prussia, the replacement of the Governor of Alsace-Lorraine with the Mayor of Straßburg, appointing a local deputy from the Centre Party as Secretary of State for Alsace-Lorraine and some other adjustments in government personnel.

Pushed by the social democrats, the government passed a widespread amnesty, under which political prisoners like Karl Liebknecht were released. Under Max von Baden, the bureaucracy, military and political leadership of the old Empire began a cooperation with the leaders of the majority parties and with the individual states of the empire. This cooperation was to have a significant impact on later events during the revolution.

In late October, the Imperial constitution was amended to transform the empire into a parliamentary monarchy. The chancellor was now responsible to the Reichstag rather than the emperor. However, Wilson's third note seemed to imply that negotiations for an armistice would be dependent on the abdication of Wilhelm II. Max and his government now feared that a military collapse and a socialist revolution at home were becoming likelier with every day that went by. In fact, the government's efforts to secure an armistice were interrupted by the Kiel mutiny, which began with events at Wilhelmshaven on 30 October and the outbreak of revolution in Germany in early November. On 1 November, Max wrote to all the ruling Princes of Germany, asking them whether they would approve of an abdication by the Emperor. On 6 November, the Chancellor sent Erzberger to conduct the negotiations with the Allies. Max, seriously ill with Spanish influenza, urged Wilhelm II to abdicate. The Emperor, who had fled from revolutionary Berlin to the Spa headquarters of the OHL in Belgium, despite similar advice by Hindenburg and Ludendorff's successor Wilhelm Groener of the OHL, was willing to consider abdication only as German Emperor, not as King of Prussia. This was not possible under the imperial constitution as it stood. Article 11 defined the empire as a confederation of states under the permanent presidency of the king of Prussia. Thus, the imperial crown was tied to the Prussian crown, and Wilhelm could not renounce one crown without renouncing the other.

Revolution and resignation
On 7 November, Max met with Friedrich Ebert, leader of the SPD, and discussed his plan to go to Spa and convince Wilhelm II to abdicate. He considered installing Prince Eitel Friedrich, Wilhelm's second son, as regent; however, the outbreak of the revolution in Berlin prevented Max from implementing his plan. Ebert decided that to keep control of the socialist uprising the Emperor must abdicate quickly and a new government was required. As the masses gathered in Berlin, at noon on 9 November 1918, Maximilian went ahead and unilaterally announced Wilhelm's abdication of both the imperial and Prussian crowns, as well as the renunciation of Crown Prince Wilhelm.

Shortly thereafter, Ebert appeared in the Reichskanzlei and demanded that the government be handed over to him and the SPD, as that was the only way to keep up law and order. In an unconstitutional move, Max resigned and appointed Ebert as his successor. On the same day, Philipp Scheidemann spontaneously proclaimed Germany a republic in order to placate the masses and prevent a socialist revolution. When Maximilian later visited Ebert to say goodbye before leaving Berlin, Ebert – who urgently wanted to keep up the old order, improving it through parliamentary rule, and head a legitimate, not a revolutionary government – asked him to stay on as regent (Reichsverweser). Maximilian refused and, turning his back on politics for good, departed for Baden.

Although events had overtaken him during his tenure at the Reichskanzlei and he was not considered a strong Chancellor, Max is seen today as having played a vital role in enabling the transition from the old regime to a democratic government based on the majority parties and the Reichstag. This made the government of Ebert that emerged from the November revolution acceptable to some conservative forces in the bureaucracy and military, which was one of Ebert's strongest aims. They were thus willing to ally themselves with him against the more radical demands by the revolutionaries on the far-left.

Later life and death
Maximilian spent the rest of his life in retirement. He rejected a mandate to the 1919 Weimar National Assembly, offered to him by the German Democratic politician Max Weber. In 1920, together with Kurt Hahn, he established the Schule Schloss Salem boarding school, which was intended to help educate a new German intellectual elite.

Max also published a number of books, assisted by Hahn: Völkerbund und Rechtsfriede (1919), Die moralische Offensive (1921) and Erinnerungen und Dokumente (1927).

In 1928, following the death of Grand Duke Frederick II, who had been deposed in November 1918 when the German monarchies were abolished, Maximilian became head of the House of Zähringen, assuming the dynasty's historical title of Margrave of Baden. He died at Salem on 6 November the following year.

Children
Maximilian was married to Princess Marie Louise of Hanover and Cumberland, eldest daughter of Ernest Augustus, Crown Prince of Hanover, and Thyra of Denmark, on 10 July 1900 in Gmunden, Austria-Hungary. The couple had two children:

 * Princess Marie Alexandra of Baden (1 August 1902 – 29 January 1944); married Prince Wolfgang of Hesse, Landgrave of Hesse-Kassel, son of Prince Frederick Charles of Hesse-Kassel, designated King of Finland, and Princess Margaret of Prussia; no issue. Marie Alexandra was killed in a bombing of Frankfurt by the Allies of World War II.
 * Prince Berthold of Baden (24 February 1906 – 27 October 1963); later Margrave of Baden; married Princess Theodora, daughter of Prince Andrew of Greece and Denmark and Princess Alice of Battenberg. Theodora was the sister of Prince Philip, Duke of Edinburgh.

Titles and styles

 * 10 July 1867 – 8 August 1928: His Grand Ducal Highness Prince Maximilian of Baden
 * 9 August 1928 – 6 November 1929: His Royal Highness The Margrave of Baden

Honours
• Baden:
 * Domestic

• * Knight of the House Order of Fidelity

• * Knight of the Order of Berthold the First

• * Knight of the Zähringer Lion, 1st Class

• * Commander of the Military Karl-Friedrich Merit Order, 1st Class, 30 August 1914

• * Friedrich-Luise Medal

• * Commemorative Medal for the Golden Jubilee of Grand Duke Friedrich I and Grand Duchess Luise

•  Anhalt: Grand Cross of Albert the Bear, 1889

•  undefined: Knight of St. Hubert, 1899

•  Hanoverian Royal Family: Knight of St. George

•    Ernestine duchies: Grand Cross of the Saxe-Ernestine House Order

•  Hesse and by Rhine: Grand Cross of the Ludwig Order, 6 May 1892

•  Mecklenburg: Grand Cross of the Wendish Crown, with Crown in Ore

•  Saxe-Weimar-Eisenach: Grand Cross of the White Falcon

•  undefined: Knight of the Rue Crown

•  Württemberg: Grand Cross of the Württemberg Crown, 1885

•  undefined:

• * Grand Cross of the Red Eagle, 27 September 1898

• * Knight of the Black Eagle, with Collar, invested 18 January 1903

• * Grand Commander's Cross of the Royal House Order of Hohenzollern

• * Iron Cross (1914), 2nd Class

•  Hohenzollern: Cross of Honour of the Princely House Order of Hohenzollern, 1st Class

 * Foreign
 * Austria-Hungary: Grand Cross of St. Stephen, 1900
 * 🇧🇪 Belgium: Grand Cordon of the Order of Leopold (military), 2 October 1906
 * undefined: Grand Cross of St. Alexander
 * 🇩🇰 Denmark: Knight of the Elephant, 10 July 1900
 * undefined: Grand Cross of the Order of Prince Danilo I
 * undefined: Knight of St. Andrew
 * 🇸🇪 🇳🇴 Sweden-Norway:
 * Grand Cross of St. Olav, 30 August 1887
 * Knight of the Seraphim, 24 April 1902

title: Prince Maximilian of Baden