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Countability of Church-Kleene ordinal in ZF

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#set-theory #axiom-of-choice
91
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Proof Writing: Regarding an equivalent statement of the Axiom of Choice. (Tao, Analysis I: Exercise 8.4.2.)

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#proof-writing #axiom-of-choice
43
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Proof Verification: Using axiom of choice correctly.

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#proof-verification #proof-writing #set-theory #axiom-of-choice
229
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Version of the Banach-Tarski Paradox for Tori

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#general-topology #axiom-of-choice
534
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Why is Axiom of Choice "a convenient and safe labour-saving device"?

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#real-analysis #analysis #set-theory #axiom-of-choice #axioms
198
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When induction proofs need a choice function

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#logic #induction #axiom-of-choice
769
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About the proof that an infinite ordinal has the same cardinality as its successor

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#set-theory #cardinals #axiom-of-choice #ordinals
128
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Constructive predicative Hausdorffification without Choice

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#general-topology #axiom-of-choice
264
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Existence of sets, power set, & axiom of choice

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#elementary-set-theory #axiom-of-choice
108
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Is Axiom of choice required to define $S = \{x_n : n \in \mathbb{Z}\}$ where $x_n=f^n(x_0)$?

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#elementary-set-theory #axiom-of-choice
1k
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Cambridge Tripos 2015: Zorn's Lemma Proof Requiring Axiom of Choice

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#set-theory #axiom-of-choice
331
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Cambridge Tripos 2015: Partial Order Extended to Total Order Proof

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#abstract-algebra #elementary-set-theory #order-theory #axiom-of-choice
273
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Equivalence of Dedekind infinity and infinity, and Axiom of Choice

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#set-theory #infinity #axiom-of-choice
320
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Well ordering principle

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#elementary-number-theory #axiom-of-choice #well-orders
97
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Verification of a proof of some equivalents of AC

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#proof-verification #set-theory #axiom-of-choice

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