Question

Looking for counterexamples where the output of a computable function always has a computably checkable property, but PA cannot prove this

score 184 · Answer 1 · 2026-03-27 21:18:07

184

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Looking for counterexamples where the output of a computable function always has a computably checkable property, but PA cannot prove this

Published on 27 Mar 2026 - 21:18

score 66 · Answer 2 · 2013-08-22 13:02:45

66

Views

Strategy to proof the existence of a number/condition

Published on 22 Aug 2013 - 13:02

score 2k · Answer 3 · 2013-08-26 00:53:26

2k

Views

Prove that no positive integer is both even and odd, and that all positive integers are either even or odd

Published on 26 Aug 2013 - 0:53

score 199 · Answer 4 · 2013-08-27 15:13:04

199

Views

Help with a proof by induction.

Published on 27 Aug 2013 - 15:13

score 259 · Answer 5 · 2013-08-30 05:48:14

259

Views

Not Skolem's Paradox - Part 2

Published on 30 Aug 2013 - 5:48

score 367 · Answer 6 · 2013-08-31 13:53:27

367

Views

Does ZFC prove a sentence in the language of arithmetic that PA+Con(ZFC) cannot prove?

Published on 31 Aug 2013 - 13:53

score 302 · Answer 7 · 2013-09-03 02:48:17

302

Views

consistency strength of PA

Published on 03 Sep 2013 - 2:48

score 2k · Answer 8 · 2013-09-10 02:28:37

2k

Views

Can we prove that odd and even numbers alternate without using induction?

Published on 10 Sep 2013 - 2:28

score 304 · Answer 9 · 2026-03-27 21:16:49

304

Views

differentiate the terms deductive system, model/structure, formal system, first-order logic

Published on 27 Mar 2026 - 21:16

score 851 · Answer 10 · 2026-03-27 21:23:03

851

Views

clarify the term "arithmetics" when talking about Gödel's incompleteness theorems

Published on 27 Mar 2026 - 21:23

score 569 · Answer 11 · 2026-03-25 15:38:53

569

Views

Why is bounded induction stronger than open induction?

Published on 25 Mar 2026 - 15:38

score 229 · Answer 12 · 2026-03-25 15:40:59

229

Views

Is open induction as strong as bounded induction without free bounds?

Published on 25 Mar 2026 - 15:40

score 173 · Answer 13 · 2026-03-25 15:45:24

173

Views

How strong is ramified predicative second-order arithmetic?

Published on 25 Mar 2026 - 15:45

score 1.8k · Answer 14 · 2013-09-17 03:13:42

1.8k

Views

Neither Even Nor Odd Natural Numbers

Published on 17 Sep 2013 - 3:13

score 709 · Answer 15 · 2013-09-17 16:36:08

709

Views

For all $y$, there exists an $x$ where $x\geq y$

Published on 17 Sep 2013 - 16:36

List Question

Looking for counterexamples where the output of a computable function always has a computably checkable property, but PA cannot prove this

Strategy to proof the existence of a number/condition

Prove that no positive integer is both even and odd, and that all positive integers are either even or odd

Help with a proof by induction.

Not Skolem's Paradox - Part 2

Does ZFC prove a sentence in the language of arithmetic that PA+Con(ZFC) cannot prove?

consistency strength of PA

Can we prove that odd and even numbers alternate without using induction?

differentiate the terms deductive system, model/structure, formal system, first-order logic

clarify the term "arithmetics" when talking about Gödel's incompleteness theorems

Why is bounded induction stronger than open induction?

Is open induction as strong as bounded induction without free bounds?

How strong is ramified predicative second-order arithmetic?

Neither Even Nor Odd Natural Numbers

For all $y$, there exists an $x$ where $x\geq y$

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