Question

Interaction of completeness and second incompleteness theorems

score 348 · Answer 1 · 2014-04-01 07:05:05

348

Views

Interaction of completeness and second incompleteness theorems

Published on 01 Apr 2014 - 7:05

score 899 · Answer 2 · 2014-04-02 23:47:36

899

Views

Con(PA) implies consistency of $\mathsf{PA}$ + ¬Con($\mathsf{PA}$)

Published on 02 Apr 2014 - 23:47

score 302 · Answer 3 · 2014-04-06 00:01:50

302

Views

Does second-order arithmetic (Z2) prove soundness and uniform reflection for first-order arithmetic (PA)?

Published on 06 Apr 2014 - 0:01

score 175 · Answer 4 · 2014-04-10 16:01:14

175

Views

Peano's theory of arithmetic and Gödel's 1st Incompleteness Theorem

Published on 10 Apr 2014 - 16:01

score 1.7k · Answer 5 · 2014-04-14 12:42:39

1.7k

Views

Must every decidable theory be axiomatizable?

Published on 14 Apr 2014 - 12:42

score 1.8k · Answer 6 · 2014-04-14 13:57:28

1.8k

Views

Modern book on Gödel's incompleteness theorems in all technical details

Published on 14 Apr 2014 - 13:57

score 620 · Answer 7 · 2014-04-16 13:01:29

620

Views

Gödel's incompleteness theorems: where to learn? Is there a straightforward relation between the two?

Published on 16 Apr 2014 - 13:01

score 401 · Answer 8 · 2026-03-25 06:03:18

401

Views

If $T$ proves any incorrect $\forall$-rudimentary sentence, then $T$ is inconsistent

Published on 25 Mar 2026 - 6:03

score 163 · Answer 9 · 2014-04-19 20:25:35

163

Views

Maths, esp. Godel, and poetry

Published on 19 Apr 2014 - 20:25

score 855 · Answer 10 · 2014-04-23 20:23:06

855

Views

Is Douglas Hofstadter's version of Godel's proof utter nonsense?

Published on 23 Apr 2014 - 20:23

score 1.6k · Answer 11 · 2014-04-27 20:19:38

1.6k

Views

Why doesn't "$V$ is a model of $ZF$" imply consistency of ZF?

Published on 27 Apr 2014 - 20:19

score 809 · Answer 12 · 2026-03-25 00:53:20

809

Views

How did Kurt Gödel's Incompleteness Theorem affect the mathematical world?

Published on 25 Mar 2026 - 0:53

score 1.1k · Answer 13 · 2014-06-02 07:59:12

1.1k

Views

Concrete example for diagonal lemma

Published on 02 Jun 2014 - 7:59

score 2.4k · Answer 14 · 2014-06-05 14:13:12

2.4k

Views

Understanding ω-consistent and ω-incomplete theory

Published on 05 Jun 2014 - 14:13

score 370 · Answer 15 · 2014-06-06 16:29:53

370

Views

Scapegoat theory and PA

Published on 06 Jun 2014 - 16:29

List Question

Interaction of completeness and second incompleteness theorems

Con(PA) implies consistency of $\mathsf{PA}$ + ¬Con($\mathsf{PA}$)

Does second-order arithmetic (Z2) prove soundness and uniform reflection for first-order arithmetic (PA)?

Peano's theory of arithmetic and Gödel's 1st Incompleteness Theorem

Must every decidable theory be axiomatizable?

Modern book on Gödel's incompleteness theorems in all technical details

Gödel's incompleteness theorems: where to learn? Is there a straightforward relation between the two?

If $T$ proves any incorrect $\forall$-rudimentary sentence, then $T$ is inconsistent

Maths, esp. Godel, and poetry

Is Douglas Hofstadter's version of Godel's proof utter nonsense?

Why doesn't "$V$ is a model of $ZF$" imply consistency of ZF?

How did Kurt Gödel's Incompleteness Theorem affect the mathematical world?

Concrete example for diagonal lemma

Understanding ω-consistent and ω-incomplete theory

Scapegoat theory and PA

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