An important and fundamental axiom in set theory sometimes called Zermelo's axiom of choice. It was formulated by Zermelo in 1904 and states that, given any set of mutually disjoint nonempty sets, there exists at least one set that contains exactly one element in common with each of the nonempty ...

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### Can we have an infinite sequence of decreasing cardinality all terms of which have equal sized power sets?

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### Are there known examples of sets whose power set is equal in size to power set of larger sets only in absence of choice?

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### When does $A^A=2^A$ without the axiom of choice?

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### Do choice principles in all generic extensions imply AC in $V$?

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### The Tall Tale of Terminating Transfinite Towers

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### Why worry about the axiom of choice?

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### The partial preorder on $\mathbb N$ generated by the finite axioms of choice

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### How to construct a basis for the dual space of an infinite dimensional vector space?

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### Is $\mathbb{R}$ a $\mathbb{C}$-module without AC?

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### The Rise and Fall of Dictators & How it Depends on Our Choice

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### Countable (?) dependent choice

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### Kaplansky's theorem and Axiom of choice

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### Are there paradoxes in ZF + (the Axiom of Choice for finite sets)? [closed]

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### Does every model of ZF-foundation have an extension, with no new well-founded sets, where every set is bijective with a well-founded set?

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### On the Choice Content of Carathéodory's Conformal Mapping Theorem

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### Graphs without maximal vertex-transivite subgraphs

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### Does constructing non-measurable sets require the axiom of choice?

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### Ascending chain of vertex-transitive graphs

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### Choosing subsets of $\mathbb R$ of cardinality $\frak c$, who wins?

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### Relations of axioms of choice

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### Are classes still “larger” than sets without the axiom of choice?

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### Can There be a 1 dimensional Banach-Tarski paradox in the absence of choice

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### Measurable functions with non measurable image

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### Does the existence of a unique chromatic (possibly transfinite) number for every (possibly non-finite) simple graph imply the axiom of choice?

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### In what ways is ZF (without Choice) “somewhat constructive”

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### Does the axiom of choice follow from the statement “Every simple undirected graph is either connected, or its complement is connected”?

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### Can we prove the epsilon theorems without the axiom of choice?

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### Forcing over models without the axiom of choice

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### A model of ZF without a well-ordering of the reals in which any two sets of reals are comparable

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### Chromatic number of a topological space

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### Is the non-triviality of the algebraic dual of an infinite-dimensional vector space equivalent to the axiom of choice?

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### Are there any non-linear solutions of Cauchy's equation ($f(x+y)=f(x)+f(y)$) without assuming the Axiom of Choice?

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### Subset of the plane that intersects every line exactly twice

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### Totally bounded spaces and axiom of choice

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### Selection in a small category

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### Cauchy real numbers with and without modulus

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### Forcing, cuts, and Dedekind-finite cardinalities

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### Consistency of a non-measurable set of reals when the continuum cannot be well-ordered

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### Objects which can't be defined without making choices but which end up independent of the choice

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### Are these large cardinals properties equivalent?

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### Do all countable $\omega$-standard models of ZF with an amorphous set have the same inclusion relation up to isomorphism?

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### Why doesn't choice imply global choice (in NBG)?

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### Choice sets and the axiom of choice

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### Undetermined games of “overdetermined” type

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### The axiom of choice as a consequence of a stronger semantics?

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### Is it known whether every $\omega$-tree with an infinite antichain has an infinite chain in $\mathsf{ZF}$?

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### Unique Existence and the Axiom of Choice

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### Hahn-Banach and the “Axiom of Probabilistic Choice”

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### Relation between well-orderings of $\mathbb{R}$, and bases over $\mathbb{Q}$

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