List questions from axiom-of-choice

Published on 25 Apr 2016 - 15:57

764

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For every cardinal $\kappa$, $\kappa^+$ is regular

Published on 25 Apr 2016 - 16:04

236

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Does the regularity of $\omega_{\alpha+1}$ need Axiom of Choice?

Published on 26 Apr 2016 - 21:50

131

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Is $\textsf{BPIT}$ equivalent to some ordering principle?

Published on 28 Apr 2016 - 6:59

102

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Existence of how many sets is asserted by the axiom of choice in this case?

Published on 29 Apr 2016 - 9:07

137

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A puzzle concerning the axiom of choice and the reals

Published on 29 Apr 2016 - 9:15

88

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Proving the Axiom of Choice is equalivalent to the statement "If $A$ can be well-ordered, then so can $\mathcal{P}(A)$."

Published on 02 May 2016 - 4:21

640

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The well-ordering principle implies Zorn's Lemma

Published on 02 May 2016 - 15:35

307

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Can every poset be toplogically sorted?

Published on 02 May 2016 - 18:03

739

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Axiom of Choice implies the Well-Ordering Principle

Published on 03 May 2016 - 23:49

156

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Are there any large cardinals that are not ordinals?

Published on 29 Mar 2026 - 9:11

1.1k

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Soft Question: Why does the Axiom of Choice lead to the weirdest constructions?

Published on 04 May 2016 - 8:59

639

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Non-principal ultrafilters on a set

Published on 04 May 2016 - 14:51

4.4k

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Why do people accept the axiom of choice given the well ordering principle?

Published on 08 May 2016 - 3:03

1.6k

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What is an example of two sets which cannot be compared?

Published on 08 May 2016 - 22:52

List Question

Using the axiom of choice to choose bijections

For every cardinal $\kappa$, $\kappa^+$ is regular

Does the regularity of $\omega_{\alpha+1}$ need Axiom of Choice?

Is $\textsf{BPIT}$ equivalent to some ordering principle?

Existence of how many sets is asserted by the axiom of choice in this case?

A puzzle concerning the axiom of choice and the reals

Proving the Axiom of Choice is equalivalent to the statement "If $A$ can be well-ordered, then so can $\mathcal{P}(A)$."

The well-ordering principle implies Zorn's Lemma

Can every poset be toplogically sorted?

Axiom of Choice implies the Well-Ordering Principle

Are there any large cardinals that are not ordinals?

Soft Question: Why does the Axiom of Choice lead to the weirdest constructions?

Non-principal ultrafilters on a set

Why do people accept the axiom of choice given the well ordering principle?

What is an example of two sets which cannot be compared?

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