Question

If a theory $A$ can prove $B$ consistent relative to $A$, and $A$ is consistent, does $B$ have to be consistent?

score 156 · Answer 1 · 2026-03-28 15:11:25

156

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If a theory $A$ can prove $B$ consistent relative to $A$, and $A$ is consistent, does $B$ have to be consistent?

Published on 28 Mar 2026 - 15:11

score 140 · Answer 2 · 2016-07-01 00:47:18

140

Views

Are the 1 dimensional loop spaces in homotopy type theory commutative?

Published on 01 Jul 2016 - 0:47

score 6.1k · Answer 3 · 2026-03-31 11:23:46

6.1k

Views

Where are the axioms?

Published on 31 Mar 2026 - 11:23

score 182 · Answer 4 · 2026-03-31 13:36:41

182

Views

Is there a way to axiomatize the category of sets and relations?

Published on 31 Mar 2026 - 13:36

score 305 · Answer 5 · 2013-04-03 11:09:07

305

Views

Hard proof concerning the periodicity of trigonometrical functions. Is that a challenge or just trivial

Published on 03 Apr 2013 - 11:09

score 702 · Answer 6 · 2026-03-25 12:17:25

702

Views

What lessons have mathematicians drawn from the existence of non-standard models?

Published on 25 Mar 2026 - 12:17

score 16.1k · Answer 7 · 2026-03-28 15:01:30

16.1k

Views

Infinite sets don't exist!?

Published on 28 Mar 2026 - 15:01

score 421 · Answer 8 · 2013-04-11 08:03:03

421

Views

Functions and metafunctions

Published on 11 Apr 2013 - 8:03

score 477 · Answer 9 · 2013-04-11 15:30:11

477

Views

Beyond Goedel incompleteness and lack of soundness/completeness of higher-order logics

Published on 11 Apr 2013 - 15:30

score 588 · Answer 10 · 2013-04-12 16:59:45

588

Views

Axioms of arithmetic and isomorphism

Published on 12 Apr 2013 - 16:59

score 1.5k · Answer 11 · 2026-03-28 13:21:19

1.5k

Views

Is the proper class of all ordinals equivalent to the potential infinity of pre-Cantor times?

Published on 28 Mar 2026 - 13:21

score 226 · Answer 12 · 2013-04-12 21:07:58

226

Views

Hilbert's Program

Published on 12 Apr 2013 - 21:07

score 242 · Answer 13 · 2013-04-14 18:39:48

242

Views

Which concept is more primary in modern formal math: set, function or natural number?

Published on 14 Apr 2013 - 18:39

score 590 · Answer 14 · 2013-04-15 04:06:08

590

Views

What of the "Sets, Classes, and Categories" approach to the foundations?

Published on 15 Apr 2013 - 4:06

score 2k · Answer 15 · 2026-02-23 06:42:25

2k

Views

Are axioms and rules of inference interchangeable?

Published on 23 Feb 2026 - 6:42

List Question

If a theory $A$ can prove $B$ consistent relative to $A$, and $A$ is consistent, does $B$ have to be consistent?

Are the 1 dimensional loop spaces in homotopy type theory commutative?

Where are the axioms?

Is there a way to axiomatize the category of sets and relations?

Hard proof concerning the periodicity of trigonometrical functions. Is that a challenge or just trivial

What lessons have mathematicians drawn from the existence of non-standard models?

Infinite sets don't exist!?

Functions and metafunctions

Beyond Goedel incompleteness and lack of soundness/completeness of higher-order logics

Axioms of arithmetic and isomorphism

Is the proper class of all ordinals equivalent to the potential infinity of pre-Cantor times?

Hilbert's Program

Which concept is more primary in modern formal math: set, function or natural number?

What of the "Sets, Classes, and Categories" approach to the foundations?

Are axioms and rules of inference interchangeable?

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