Question

Godel's incompleteness theorem and proof by contradiction

score 117 · Answer 1 · 2022-11-08 15:11:40

Godel's incompleteness theorem and proof by contradiction

Published on 08 Nov 2022 - 15:11

score 33 · Answer 2 · 2022-11-15 13:10:53

Is there a formal system that proves its consistency while proving the existence of a stronger formal system that can interpret general recursion too?

score 205 · Answer 3 · 2022-12-06 14:22:57

205

Views

Is there a formal definition of a number theoretical statement which is self-referential?

Published on 06 Dec 2022 - 14:22

score 31 · Answer 4 · 2022-12-16 04:38:43

31

Views

Are many generalized formula unprovable (related to Godel's first incompleteness theorem)?

Published on 16 Dec 2022 - 4:38

score 54 · Answer 5 · 2026-03-28 06:48:35

54

Views

The word problem for groups preceded PH Theorem as a practical undecidability result

Published on 28 Mar 2026 - 6:48

score 47 · Answer 6 · 2026-02-24 08:20:34

47

Views

Theory of real numbers is decidable but Peano arithmetic is undecidable?

Published on 24 Feb 2026 - 8:20

score 179 · Answer 7 · 2026-02-24 08:18:54

179

Views

Is "$X$ is finite" decidable (in ZFC)?

Published on 24 Feb 2026 - 8:18

score 66 · Answer 8 · 2023-01-07 13:45:42

66

Views

Incompletness and infinite induction

Published on 07 Jan 2023 - 13:45

score 66 · Answer 9 · 2023-01-09 13:35:53

66

Views

How does consistency PA+¬Con(PA) implies consistency of PA?

Published on 09 Jan 2023 - 13:35

score 57 · Answer 10 · 2023-01-10 18:03:08

57

Views

Arithmetic theory $T$ such that $U = T + \operatorname{Con}_{T}$ is consistent, but $T + \operatorname{Con}_{U}$ is not.

Published on 10 Jan 2023 - 18:03

score 99 · Answer 11 · 2026-03-27 01:46:26

99

Views

Why is it specified in the 2nd incompleteness theorem that a system of arithmetic cannot prove its own consistency?

Published on 27 Mar 2026 - 1:46

score 141 · Answer 12 · 2026-03-25 20:12:43

141

Views

Extending a Model of $ T + \operatorname {Con} ( T ) $ to a model of $ T + \neg \operatorname {Con} ( T ) $

Published on 25 Mar 2026 - 20:12

List Question

Godel's incompleteness theorem and proof by contradiction

Is there a formal system that proves its consistency while proving the existence of a stronger formal system that can interpret general recursion too?

Is there a formal definition of a number theoretical statement which is self-referential?

Are many generalized formula unprovable (related to Godel's first incompleteness theorem)?

The word problem for groups preceded PH Theorem as a practical undecidability result

Theory of real numbers is decidable but Peano arithmetic is undecidable?

Is "$X$ is finite" decidable (in ZFC)?

Incompletness and infinite induction

How does consistency PA+¬Con(PA) implies consistency of PA?

Arithmetic theory $T$ such that $U = T + \operatorname{Con}_{T}$ is consistent, but $T + \operatorname{Con}_{U}$ is not.

Why is it specified in the 2nd incompleteness theorem that a system of arithmetic cannot prove its own consistency?

Extending a Model of $ T + \operatorname {Con} ( T ) $ to a model of $ T + \neg \operatorname {Con} ( T ) $

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