List questions from axiom-of-choice

Published on 29 Mar 2026 - 2:36

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How does one prove $ZF\vDash MC\Rightarrow AC$?

Published on 09 Sep 2014 - 13:58

249

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Does there exist a connected 2-regular uncountable graph, or an uncountable path?

Published on 27 Mar 2026 - 22:01

345

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Existence of non measurable set and ZF theory?

Published on 11 Sep 2014 - 11:58

580

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What is needed to make Euclidean spaces isomorphic as groups?

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Countable union of countable sets is countable and AC (or axiom of countable choice)

Published on 23 Sep 2014 - 16:19

121

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Basis in topology and AC

Published on 23 Sep 2014 - 16:54

148

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Dedekind finite set and a special well ordered set

Published on 29 Mar 2026 - 3:45

442

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Existence of a basis in constructive vector spaces

Published on 26 Mar 2026 - 1:01

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Over ZF, does "every Hilbert space have a basis" imply AC?

Published on 30 Sep 2014 - 0:04

595

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How big can the continuum be without choice?

Published on 02 Oct 2014 - 16:23

424

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Does the existence of a recursive sequence that involves an arbitrary choice at every step require the axiom of choice?

Published on 28 Mar 2026 - 7:45

288

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Can a $\mathbf{Q}$-basis of $\mathbf{R}$ be explicitly defined?

Published on 30 Mar 2026 - 0:19

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Existence of non-trivial linear functional on any vector space

Published on 12 Oct 2014 - 14:07

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Cardinality of the union of two infinite set

Published on 18 Oct 2014 - 3:24

List Question

Infinite Set has greater or equal cardinality that of N

How does one prove $ZF\vDash MC\Rightarrow AC$?

Does there exist a connected 2-regular uncountable graph, or an uncountable path?

Existence of non measurable set and ZF theory?

What is needed to make Euclidean spaces isomorphic as groups?

Countable union of countable sets is countable and AC (or axiom of countable choice)

Basis in topology and AC

Dedekind finite set and a special well ordered set

Existence of a basis in constructive vector spaces

Over ZF, does "every Hilbert space have a basis" imply AC?

How big can the continuum be without choice?

Does the existence of a recursive sequence that involves an arbitrary choice at every step require the axiom of choice?

Can a $\mathbf{Q}$-basis of $\mathbf{R}$ be explicitly defined?

Existence of non-trivial linear functional on any vector space

Cardinality of the union of two infinite set

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