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How can one prove the axiom of collection in ZFC without using the axiom of foundation?

score 640 · Answer 1 · 2026-03-30 16:57:26

640

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How can one prove the axiom of collection in ZFC without using the axiom of foundation?

Published on 30 Mar 2026 - 16:57

score 2.7k · Answer 2 · 2026-03-30 16:54:23

2.7k

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Why do we want the Axiom of the Power Set?

Published on 30 Mar 2026 - 16:54

score 674 · Answer 3 · 2016-01-20 09:01:05

674

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Step 6, Appendix to Chapter 1 in Baby Rudin: How to show that if $\alpha > 0^$ and $\beta > 0^$, then $\alpha \beta > 0^*$?

Published on 20 Jan 2016 - 9:01

score 1.8k · Answer 4 · 2016-01-21 12:32:28

1.8k

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Prob. 6, Chap. 1, in Rudin's PMA

Published on 21 Jan 2016 - 12:32

score 1k · Answer 5 · 2026-03-27 23:39:04

1k

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Can the Recursion Theorem be proved in Peano Arithmetic?

Published on 27 Mar 2026 - 23:39

score 1.1k · Answer 6 · 2016-01-22 09:02:01

1.1k

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Prob. 7, Chap. 1, in Baby Rudin: The Existence of Logarithms

Published on 22 Jan 2016 - 9:02

score 1.3k · Answer 7 · 2026-03-30 20:44:12

1.3k

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Proof that the minimal inductive set does not contain any more elements than $\{\emptyset, s(\emptyset), s(s(\emptyset)),s(s(s(\emptyset))),...\}$?

Published on 30 Mar 2026 - 20:44

score 974 · Answer 8 · 2016-01-28 22:37:18

974

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Continuum Hypothesis in formalized language.

Published on 28 Jan 2016 - 22:37

score 347 · Answer 9 · 2016-01-30 21:05:07

347

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Theorems not Formulable in Set Theory

Published on 30 Jan 2016 - 21:05

score 663 · Answer 10 · 2016-02-01 09:46:07

663

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Can one use the Hilbert-Ackermann Consistency Theorem to prove the consistency of $PRA$?

Published on 01 Feb 2016 - 9:46

score 2.9k · Answer 11 · 2016-02-01 15:24:02

2.9k

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What is the denial of a statement in logic math?

Published on 01 Feb 2016 - 15:24

score 315 · Answer 12 · 2016-02-03 19:07:30

315

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Book on foundational reasoning of standard arithmetics "curriculum"

Published on 03 Feb 2016 - 19:07

score 67 · Answer 13 · 2016-02-12 01:38:13

67

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Bijective map on $(\Bbb N \times\Bbb N)/R$

Published on 12 Feb 2016 - 1:38

score 112 · Answer 14 · 2026-03-26 21:01:49

112

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Yoneda Lemma and foundations

Published on 26 Mar 2026 - 21:01

score 1.2k · Answer 15 · 2026-02-25 23:47:27

1.2k

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Will Homotopy Type Theory ever be as accessible as traditional Set Theory?

Published on 25 Feb 2026 - 23:47

List Question

How can one prove the axiom of collection in ZFC without using the axiom of foundation?

Why do we want the Axiom of the Power Set?

Step 6, Appendix to Chapter 1 in Baby Rudin: How to show that if $\alpha > 0^$ and $\beta > 0^$, then $\alpha \beta > 0^*$?

Prob. 6, Chap. 1, in Rudin's PMA

Can the Recursion Theorem be proved in Peano Arithmetic?

Prob. 7, Chap. 1, in Baby Rudin: The Existence of Logarithms

Proof that the minimal inductive set does not contain any more elements than $\{\emptyset, s(\emptyset), s(s(\emptyset)),s(s(s(\emptyset))),...\}$?

Continuum Hypothesis in formalized language.

Theorems not Formulable in Set Theory

Can one use the Hilbert-Ackermann Consistency Theorem to prove the consistency of $PRA$?

What is the denial of a statement in logic math?

Book on foundational reasoning of standard arithmetics "curriculum"

Bijective map on $(\Bbb N \times\Bbb N)/R$

Yoneda Lemma and foundations

Will Homotopy Type Theory ever be as accessible as traditional Set Theory?

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