List questions from axiom-of-choice

Published on 18 May 2014 - 17:19

47

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If $|X|<|Y|$ then $|Y|=|Y-X|$ (with $Y$ infinite)

Published on 28 Mar 2026 - 12:02

101

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Hilbert space without the projection theorem

Published on 18 May 2014 - 23:20

1.6k

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Fields whose algebraic closure cannot be constructed without the axiom of choice

Published on 20 May 2014 - 23:29

139

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Is there such a thing as "completion with respect to the axiom of choice?"

Published on 22 May 2014 - 12:18

504

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What do you need to know about ordinals to understand Zorn's Lemma's proof?

Published on 27 Mar 2026 - 4:58

778

Views

factorial of infinite Cardinals

Published on 28 Mar 2026 - 13:41

323

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Is it possible that $2^n=3^n$ for some Dedekind-finite cardinal $n\gt0$?

Published on 28 Mar 2026 - 13:41

407

Views

Connectedness of parts used in the Banach–Tarski paradox

Published on 25 Mar 2026 - 12:28

59

Views

Continuous is sequentially continuous

Published on 30 May 2014 - 9:27

2.7k

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Inner product on $C(\mathbb R)$

Published on 30 May 2014 - 11:18

951

Views

Examples of theorems that haven't been proven without AC in practice but can be proven without it in principle

Published on 27 Mar 2026 - 7:17

98

Views

On those behaviors of continuum function which imply the axiom of choice

Published on 28 Mar 2026 - 16:58

362

Views

Is Kunen's claim about non-equivalent forms of Axiom of Choice, true?

Published on 31 May 2014 - 0:32

605

Views

Paradoxical models of $\sf ZF$ without choice

Published on 25 Mar 2026 - 10:55

List Question

If $A$ is D-Infinite then $|P_{\infty}(A)|=|P(A)|$

If $|X|<|Y|$ then $|Y|=|Y-X|$ (with $Y$ infinite)

Hilbert space without the projection theorem

Fields whose algebraic closure cannot be constructed without the axiom of choice

Is there such a thing as "completion with respect to the axiom of choice?"

What do you need to know about ordinals to understand Zorn's Lemma's proof?

factorial of infinite Cardinals

Is it possible that $2^n=3^n$ for some Dedekind-finite cardinal $n\gt0$?

Connectedness of parts used in the Banach–Tarski paradox

Continuous is sequentially continuous

Inner product on $C(\mathbb R)$

Examples of theorems that haven't been proven without AC in practice but can be proven without it in principle

On those behaviors of continuum function which imply the axiom of choice

Is Kunen's claim about non-equivalent forms of Axiom of Choice, true?

Paradoxical models of $\sf ZF$ without choice

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