List questions from axiom-of-choice

Published on 04 Dec 2022 - 22:48

132

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A weak version of König's Theorem - Does this depend on Choice?

Published on 05 Dec 2022 - 11:11

314

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Does “Riemann integrable $\Rightarrow$ discontinuity set is measure zero” need axiom of choice?

Published on 08 Apr 2026 - 9:26

154

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Does "Lebesgue null sets is closed under countable union" need the axiom of choice?

Published on 06 Dec 2022 - 12:48

126

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Why does this proof of the Schröder Bernstein Theorem work?

Published on 06 Dec 2022 - 19:31

82

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Axiom of choice required?

Published on 15 Dec 2022 - 14:58

145

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Choice in the non-smooth Whitney Embedding Theorem

Published on 26 Mar 2026 - 12:13

97

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Is induction strictly required to prove finite AC?

Published on 08 Apr 2026 - 17:03

99

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Proof that membership is well-founded in NBG without axiom of choice

Published on 31 Dec 2022 - 13:55

111

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Explicit norm on $C([0,1])$ not dominated by $\|\cdot\|_\infty$?

Published on 01 Jan 2023 - 9:53

164

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Axiom of choice in infinitary logic

Published on 02 Jan 2023 - 12:42

177

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Defining subcategories and axiom of choice

Published on 03 Jan 2023 - 22:37

68

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In ZF, can it be proven that a non-trivial real vector space has a non-zero linear functional?

Published on 04 Jan 2023 - 3:58

90

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$AC_\omega$ is weaker than $AC$, though not provable in ZF without $AC$?

Published on 05 Apr 2026 - 7:36

167

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Proof verification that the Hahn Banach theorem equivalent to existence of a finitely additive measure for boolean algebra over ZF

Published on 26 Mar 2026 - 23:10

List Question

Why do we work in ZFC, and not ZF+CH?

A weak version of König's Theorem - Does this depend on Choice?

Does “Riemann integrable $\Rightarrow$ discontinuity set is measure zero” need axiom of choice?

Does "Lebesgue null sets is closed under countable union" need the axiom of choice?

Why does this proof of the Schröder Bernstein Theorem work?

Axiom of choice required?

Choice in the non-smooth Whitney Embedding Theorem

Is induction strictly required to prove finite AC?

Proof that membership is well-founded in NBG without axiom of choice

Explicit norm on $C([0,1])$ not dominated by $\|\cdot\|_\infty$?

Axiom of choice in infinitary logic

Defining subcategories and axiom of choice

In ZF, can it be proven that a non-trivial real vector space has a non-zero linear functional?

$AC_\omega$ is weaker than $AC$, though not provable in ZF without $AC$?

Proof verification that the Hahn Banach theorem equivalent to existence of a finitely additive measure for boolean algebra over ZF

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