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Cardinality of union of ${{\aleph }_{0}}$ disjoint sets of cardinality $\mathfrak{c}$

score 2.7k · Answer 1 · 2011-08-12 16:40:38

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Cardinality of union of ${{\aleph }_{0}}$ disjoint sets of cardinality $\mathfrak{c}$

Published on 12 Aug 2011 - 16:40

score 3.4k · Answer 2 · 2026-03-29 10:37:16

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Proving "every set can be totally ordered" without using Axiom of Choice

Published on 29 Mar 2026 - 10:37

score 1.5k · Answer 3 · 2011-08-22 14:41:02

1.5k

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Can one avoid AC in the proof that in Noetherian rings there is a maximal element for each set?

Published on 22 Aug 2011 - 14:41

score 3.9k · Answer 4 · 2011-08-28 06:02:00

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Infinite Set is Disjoint Union of Two Infinite Sets

Published on 28 Aug 2011 - 6:02

score 11k · Answer 5 · 2011-08-28 18:30:57

11k

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What is the set-theoretic definition of a function?

Published on 28 Aug 2011 - 18:30

score 805 · Answer 6 · 2011-08-31 03:51:23

805

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Descriptions of sets and the Axiom of Choice

Published on 31 Aug 2011 - 3:51

score 688 · Answer 7 · 2011-09-03 15:38:35

688

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When to use Zorn's Lemma

Published on 03 Sep 2011 - 15:38

score 417 · Answer 8 · 2011-09-08 01:49:52

417

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Equivalent formulations of Global Choice in NBG (without Foundation)

Published on 08 Sep 2011 - 1:49

score 457 · Answer 9 · 2011-09-12 22:26:28

457

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Truth Value of Theorems in Axiomatic Set Theory

Published on 12 Sep 2011 - 22:26

score 1.5k · Answer 10 · 2011-09-13 18:43:57

1.5k

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Finite choice without AC

Published on 13 Sep 2011 - 18:43

score 177 · Answer 11 · 2011-09-20 13:45:35

177

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Is $\operatorname{Hom}_A(M,N)$ a set without axiom of choice?

Published on 20 Sep 2011 - 13:45

score 4.4k · Answer 12 · 2011-09-22 04:00:29

4.4k

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Is Zorn's lemma required to prove the existence of a maximal atlas on a manifold?

Published on 22 Sep 2011 - 4:00

score 609 · Answer 13 · 2011-09-26 13:41:41

609

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Using Axiom of Choice To Find Decreasing Sequences in Linear Orders

Published on 26 Sep 2011 - 13:41

score 2.1k · Answer 14 · 2011-10-06 02:53:16

2.1k

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Uncountable Sets that can not be expressed as a disjoint union of two Uncountable sets

Published on 06 Oct 2011 - 2:53

score 4.3k · Answer 15 · 2011-10-08 20:47:57

4.3k

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Cardinality of an infinite union of finite sets

Published on 08 Oct 2011 - 20:47

List Question

Cardinality of union of ${{\aleph }_{0}}$ disjoint sets of cardinality $\mathfrak{c}$

Proving "every set can be totally ordered" without using Axiom of Choice

Can one avoid AC in the proof that in Noetherian rings there is a maximal element for each set?

Infinite Set is Disjoint Union of Two Infinite Sets

What is the set-theoretic definition of a function?

Descriptions of sets and the Axiom of Choice

When to use Zorn's Lemma

Equivalent formulations of Global Choice in NBG (without Foundation)

Truth Value of Theorems in Axiomatic Set Theory

Finite choice without AC

Is $\operatorname{Hom}_A(M,N)$ a set without axiom of choice?

Is Zorn's lemma required to prove the existence of a maximal atlas on a manifold?

Using Axiom of Choice To Find Decreasing Sequences in Linear Orders

Uncountable Sets that can not be expressed as a disjoint union of two Uncountable sets

Cardinality of an infinite union of finite sets

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