Newbetuts

In ZF, does the ring of continuous functions $C([0,1], \mathbb{R})$ have prime ideals which is not maximal?

(Long) Detailed Proof of Kőnig's Lemma (Explicit, Down to Axiom of Choice)

Bourbaki Proof of Zorn's Lemma in Lang's Algebra

Can Tarski's circle squaring problem be solved with measurable sets and/or without the Axiom of Choice?

Given a field $\mathbb F$, is there a smallest field $\mathbb G\supseteq\mathbb F$ where every element in $\mathbb G$ has an $n$th root for all $n$?

Does the principle of schematic dependent choice follow from ZFCU?

Can we define any metric on $\Bbb{R^\omega}$ so that it represents a norm?

Does the splitting lemma hold without the axiom of choice?

If a set $S$ has a choice function, does $\bigcup S$ have one too?

What does a well ordering of $\mathbb{R}$ look like? [duplicate]

Is there any example of a non-measurable set whose proof of existence doesn't appeal to the Axiom of choice?

Compact metric spaces is second countable and axiom of countable choice

Unions and the axiom of choice.

In ZF, does there exist an ordinal of provably uncountable cofinality?

Why does the infinite prisoners and hats puzzle require the axiom of choice?

Can $\mathbb{R}$ be written as an ascending union of proper additive subgroups?

New posts in axiom-of-choice

Axiom of Choice - Type Theory (Proof)

Martin's Axiom and Choice principles

Does well-ordering of the proper class of cardinal numbers imply choice?

In ZF, does the ring of continuous functions $C([0,1], \mathbb{R})$ have prime ideals which is not maximal?

(Long) Detailed Proof of Kőnig's Lemma (Explicit, Down to Axiom of Choice)

Bourbaki Proof of Zorn's Lemma in Lang's Algebra

Can Tarski's circle squaring problem be solved with measurable sets and/or without the Axiom of Choice?

Given a field $\mathbb F$, is there a smallest field $\mathbb G\supseteq\mathbb F$ where every element in $\mathbb G$ has an $n$th root for all $n$?

Does the principle of schematic dependent choice follow from ZFCU?

Can we define any metric on $\Bbb{R^\omega}$ so that it represents a norm?

Does the splitting lemma hold without the axiom of choice?

If a set $S$ has a choice function, does $\bigcup S$ have one too?

What does a well ordering of $\mathbb{R}$ look like? [duplicate]

Is there any example of a non-measurable set whose proof of existence doesn't appeal to the Axiom of choice?

Compact metric spaces is second countable and axiom of countable choice

Unions and the axiom of choice.

In ZF, does there exist an ordinal of provably uncountable cofinality?

Why does the infinite prisoners and hats puzzle require the axiom of choice?

Can $\mathbb{R}$ be written as an ascending union of proper additive subgroups?