List questions from axiom-of-choice

Published on 26 Mar 2026 - 23:11

220

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Where can I find the proof that the axiom of choice is equivalent to "every set is a projective object in $\bf Set$"?

Published on 29 Nov 2017 - 4:55

257

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Stone–Čech compactification and AC

Published on 27 Mar 2026 - 6:15

492

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Uncountable closed set of reals biject with reals without replacement or choice

Published on 28 Mar 2026 - 22:28

2.8k

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Examples of Axiom of Choice used in introductory-level undergradute math

Published on 02 Dec 2017 - 3:00

232

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Finding a Schauder basis in a countable generating subset without Zorn's lemma

Published on 25 Mar 2026 - 20:35

106

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Do we have $|\mathcal P(X)|=|X^X|$ in ZF?

Published on 05 Dec 2017 - 3:21

81

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If I say "let $x_0$ be a point of global maximum...", am I using axiom of choice?

Published on 06 Dec 2017 - 15:20

360

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Do cardinals in ZF have lattice operations?

Published on 02 Apr 2026 - 2:42

53

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Algebraic equivalent of AC

Published on 08 Dec 2017 - 12:18

380

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The 'Lying over theorem' for integral ring extension without Zorn's Lemma, when the fields of fraction are a finite extension

Published on 16 Dec 2017 - 12:42

428

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Prove that $\mathcal{P}(\mathbb{N})\setminus\{\emptyset\}$ has a choice function.

Published on 17 Dec 2017 - 18:45

1.9k

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The Hahn-Banach theorem and the axiom of choice

Published on 26 Mar 2026 - 1:25

49

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Simple Finite Application of Dependent Choice

Published on 27 Dec 2017 - 21:16

284

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Prob. 5, Sec. 10, in Munkres' TOPOLOGY, 2nd ed: The well-ordering theorem implies the choice axiom

Published on 27 Mar 2026 - 14:03

List Question

About the real closure of a field

Where can I find the proof that the axiom of choice is equivalent to "every set is a projective object in $\bf Set$"?

Stone–Čech compactification and AC

Uncountable closed set of reals biject with reals without replacement or choice

Examples of Axiom of Choice used in introductory-level undergradute math

Finding a Schauder basis in a countable generating subset without Zorn's lemma

Do we have $|\mathcal P(X)|=|X^X|$ in ZF?

If I say "let $x_0$ be a point of global maximum...", am I using axiom of choice?

Do cardinals in ZF have lattice operations?

Algebraic equivalent of AC

The 'Lying over theorem' for integral ring extension without Zorn's Lemma, when the fields of fraction are a finite extension

Prove that $\mathcal{P}(\mathbb{N})\setminus\{\emptyset\}$ has a choice function.

The Hahn-Banach theorem and the axiom of choice

Simple Finite Application of Dependent Choice

Prob. 5, Sec. 10, in Munkres' TOPOLOGY, 2nd ed: The well-ordering theorem implies the choice axiom

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