Question

Logic soundness and completeness

score 435 · Answer 1 · 2014-03-06 15:57:23

435

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Logic soundness and completeness

Published on 06 Mar 2014 - 15:57

score 640 · Answer 2 · 2017-04-11 22:38:43

640

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Is Peano arithmetic consistent in predicate logic? If so, what are the implications?

Published on 11 Apr 2017 - 22:38

score 327 · Answer 3 · 2017-04-16 01:18:17

327

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Why is Form$(x)$ a Primitive recursive relation?

Published on 16 Apr 2017 - 1:18

score 103 · Answer 4 · 2026-03-26 12:37:56

103

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primitive recursively axiomatized consistent extension of $PA$. Give sufficient conditions to make statement true

Published on 26 Mar 2026 - 12:37

score 192 · Answer 5 · 2017-04-18 19:14:55

192

Views

Problem in this step in Gödel's Completeness Theorem

Published on 18 Apr 2017 - 19:14

score 38 · Answer 6 · 2017-04-19 19:30:42

38

Views

MathLogic: Difference between proof-in-T and proof relation of T.

Published on 19 Apr 2017 - 19:30

score 141 · Answer 7 · 2017-04-20 01:52:04

141

Views

MathLogic: $T\vdash Prv^{}(\ulcorner\varphi\urcorner)\rightarrow \neg Prv^{}(\ulcorner\neg\varphi\urcorner)$

Published on 20 Apr 2017 - 1:52

score 284 · Answer 8 · 2017-04-24 22:50:52

284

Views

Incompleteness of Mendelson's Axiom System w/o 3rd Axiom

Published on 24 Apr 2017 - 22:50

score 338 · Answer 9 · 2017-04-30 05:57:11

338

Views

Can ZFC provide a truth theory for arithmetic, and express arithmetic truth?

Published on 30 Apr 2017 - 5:57

score 303 · Answer 10 · 2026-02-23 15:33:08

303

Views

Which "natural" problems are independent of ZFC?

Published on 23 Feb 2026 - 15:33

score 115 · Answer 11 · 2017-05-05 22:10:19

115

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If $T\vdash \alpha\rightarrow \Box\neg\alpha$ and $T\vdash \alpha$ then $T$ is $\omega$-inconsistent

Published on 05 May 2017 - 22:10

score 103 · Answer 12 · 2017-05-06 18:13:30

103

Views

Show that the ring $\left(\mathbb{Z}, 0, 1, +, *\right)$ admits of tuple coding by Gödel's $\beta$ function

Published on 06 May 2017 - 18:13

score 311 · Answer 13 · 2026-03-26 09:42:50

311

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What portion of mathematical statements are ZFC undecidable?

Published on 26 Mar 2026 - 9:42

score 278 · Answer 14 · 2017-05-23 14:06:14

278

Views

book recommendation for mathematical logic - especially about formal system

Published on 23 May 2017 - 14:06

score 416 · Answer 15 · 2017-05-29 13:44:32

416

Views

True, but unprovable statements and the Hydra problem. (Gödel's incompleteness)

Published on 29 May 2017 - 13:44

List Question

Logic soundness and completeness

Is Peano arithmetic consistent in predicate logic? If so, what are the implications?

Why is Form$(x)$ a Primitive recursive relation?

primitive recursively axiomatized consistent extension of $PA$. Give sufficient conditions to make statement true

Problem in this step in Gödel's Completeness Theorem

MathLogic: Difference between proof-in-T and proof relation of T.

MathLogic: $T\vdash Prv^{}(\ulcorner\varphi\urcorner)\rightarrow \neg Prv^{}(\ulcorner\neg\varphi\urcorner)$

Incompleteness of Mendelson's Axiom System w/o 3rd Axiom

Can ZFC provide a truth theory for arithmetic, and express arithmetic truth?

Which "natural" problems are independent of ZFC?

If $T\vdash \alpha\rightarrow \Box\neg\alpha$ and $T\vdash \alpha$ then $T$ is $\omega$-inconsistent

Show that the ring $\left(\mathbb{Z}, 0, 1, +, *\right)$ admits of tuple coding by Gödel's $\beta$ function

What portion of mathematical statements are ZFC undecidable?

book recommendation for mathematical logic - especially about formal system

True, but unprovable statements and the Hydra problem. (Gödel's incompleteness)

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