Question

Proving Dedekind finite implies finite assuming countable choice

score 1.9k · Answer 1 · 2012-12-03 17:46:45

1.9k

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Proving Dedekind finite implies finite assuming countable choice

Published on 03 Dec 2012 - 17:46

score 330 · Answer 2 · 2012-12-04 07:58:38

330

Views

Why can countable recursive constructions not be done using countable choice?

Published on 04 Dec 2012 - 7:58

score 243 · Answer 3 · 2012-12-04 10:57:50

243

Views

Proof that recursive construction is equivalent to dependent choice

Published on 04 Dec 2012 - 10:57

score 183 · Answer 4 · 2012-12-04 18:36:44

183

Views

Questions about generalizations of the Principle of Dependent Choices

Published on 04 Dec 2012 - 18:36

score 193 · Answer 5 · 2026-04-02 20:14:25

193

Views

Question about trees and generalizing the Principle of Dependent Choices.

Published on 02 Apr 2026 - 20:14

score 60 · Answer 6 · 2012-12-05 09:52:22

60

Views

Axiom of choice on function

Published on 05 Dec 2012 - 9:52

score 1.3k · Answer 7 · 2012-12-05 11:46:53

1.3k

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What's the difference between saying that there is no cardinal between $\aleph_0$ and $\aleph_1$ as opposed to saying that...

Published on 05 Dec 2012 - 11:46

score 4.6k · Answer 8 · 2012-12-05 18:40:12

4.6k

Views

Simple and intuitive example for Zorns Lemma

Published on 05 Dec 2012 - 18:40

score 1.6k · Answer 9 · 2012-12-06 13:06:54

1.6k

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Using Zorn's Lemma to show that a filter is contained in an ultrafilter

Published on 06 Dec 2012 - 13:06

score 257 · Answer 10 · 2012-12-07 13:02:02

What's the thorny issue on: "If all $S\in \ell $ are nonempty, does it follow that $\prod_{S\in \ell} S$ is nonempty? when $\ell$ is infinite?"

score 135 · Answer 11 · 2012-12-07 14:55:21

135

Views

Theorem's relying on algebraic closures

Published on 07 Dec 2012 - 14:55

score 620 · Answer 12 · 2012-12-08 18:36:55

620

Views

Does negation of Axiom of Choice imply symmetry?

Published on 08 Dec 2012 - 18:36

score 275 · Answer 13 · 2012-12-08 21:22:01

275

Views

Problem 1.30 (The Maximum Principle is equivalent to the axiom of choice) (J.Bell, Boolean-valued Models and Independence Proofs, 3rd edition)

Published on 08 Dec 2012 - 21:22

score 206 · Answer 14 · 2012-12-09 04:46:09

206

Views

Cardinality of $\mathbb R\setminus\mathbb Q$ without AC

Published on 09 Dec 2012 - 4:46

score 708 · Answer 15 · 2012-12-11 20:15:26

708

Views

Axiom of Choice - Naive Counterexample

Published on 11 Dec 2012 - 20:15

List Question

Proving Dedekind finite implies finite assuming countable choice

Why can countable recursive constructions not be done using countable choice?

Proof that recursive construction is equivalent to dependent choice

Questions about generalizations of the Principle of Dependent Choices

Question about trees and generalizing the Principle of Dependent Choices.

Axiom of choice on function

What's the difference between saying that there is no cardinal between $\aleph_0$ and $\aleph_1$ as opposed to saying that...

Simple and intuitive example for Zorns Lemma

Using Zorn's Lemma to show that a filter is contained in an ultrafilter

What's the thorny issue on: "If all $S\in \ell $ are nonempty, does it follow that $\prod_{S\in \ell} S$ is nonempty? when $\ell$ is infinite?"

Theorem's relying on algebraic closures

Does negation of Axiom of Choice imply symmetry?

Problem 1.30 (The Maximum Principle is equivalent to the axiom of choice) (J.Bell, Boolean-valued Models and Independence Proofs, 3rd edition)

Cardinality of $\mathbb R\setminus\mathbb Q$ without AC

Axiom of Choice - Naive Counterexample

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