List questions from axiom-of-choice

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Is there any motivation for Zorn's Lemma?

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Why is the axiom of choice separated from the other axioms?

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Why don't you need the Axiom of Choice when constructing the "inverse" of an injection?

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Can one construct a non-measurable set without Axiom of choice?

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Given an injection $\mathbb{N}\to\mathcal{P}(X)$, how can we construct a surjection $X\to\mathbb{N}$?

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What is the smallest possible value of $\omega_1$ in $\mathrm{ZF}$?

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Axiom of choice and calculus

Published on 06 May 2012 - 8:52

List Question

Continuity and the Axiom of Choice

Bourbaki-Witt fixed point theorem: two questions

Is a chain-complete lattice a complete lattice without the axiom of choice?

Is there any motivation for Zorn's Lemma?

Why is the axiom of choice separated from the other axioms?

Why don't you need the Axiom of Choice when constructing the "inverse" of an injection?

Do We Need the Axiom of Choice for Finite Sets?

Can one construct a non-measurable set without Axiom of choice?

Prove that every set with more than one element has a permutation without fixed points

Tukey's lemma by axiom of choice

What is a basis for the vector space of continuous functions?

Constructing a subset not in $\mathcal{B}(\mathbb{R})$ explicitly

Given an injection $\mathbb{N}\to\mathcal{P}(X)$, how can we construct a surjection $X\to\mathbb{N}$?

What is the smallest possible value of $\omega_1$ in $\mathrm{ZF}$?

Axiom of choice and calculus

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