Question

Axiomatic system and Hilbert's 2nd problem

score 499 · Answer 1 · 2012-09-04 20:43:24

499

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Axiomatic system and Hilbert's 2nd problem

Published on 04 Sep 2012 - 20:43

score 455 · Answer 2 · 2026-03-26 11:06:42

455

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Can decidability results for monadic second-order logic be extended to monadic higher-order logics?

Published on 26 Mar 2026 - 11:06

score 3.4k · Answer 3 · 2026-03-26 12:34:54

3.4k

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are there non-standard models of arithmetic in second order arithmetic?

Published on 26 Mar 2026 - 12:34

score 6.3k · Answer 4 · 2012-10-01 17:43:09

6.3k

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What is the prerequisite knowledge for learning Godel's incompleteness theorem

Published on 01 Oct 2012 - 17:43

score 4.8k · Answer 5 · 2012-10-07 14:26:54

4.8k

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Can we prove that a statement cannot be proved?

Published on 07 Oct 2012 - 14:26

score 4.7k · Answer 6 · 2012-10-13 20:05:03

4.7k

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What does it mean for something to be true but not provable in peano arithmetic?

Published on 13 Oct 2012 - 20:05

score 186 · Answer 7 · 2012-10-24 18:24:30

186

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Provability becoming decidable in a larger system?

Published on 24 Oct 2012 - 18:24

score 275 · Answer 8 · 2012-11-01 18:53:09

275

Views

Given a φ independent of PA which is true in the standard model, will always (PA+ ¬φ) be ω-inconsistent?

Published on 01 Nov 2012 - 18:53

score 89 · Answer 9 · 2012-11-03 00:30:54

89

Views

Given a φ independent of PA which is true in the standard model, will always (PA+ ¬φ) be Σn-unsound for some n?

Published on 03 Nov 2012 - 0:30

score 10k · Answer 10 · 2012-11-04 10:54:09

10k

Views

Does Gödel's Incompleteness Theorem really say anything about the limitations of theoretical physics?

Published on 04 Nov 2012 - 10:54

score 349 · Answer 11 · 2012-11-04 23:27:46

349

Views

What is it wrong in this argument about the interpretability hierarchy?

Published on 04 Nov 2012 - 23:27

score 327 · Answer 12 · 2026-03-26 11:00:44

327

Views

Is every φ above the second level of the arithmetical hierarchy independent of PA?

Published on 26 Mar 2026 - 11:00

score 119 · Answer 13 · 2012-11-27 03:59:10

119

Views

Is there a mechanical procedure within PA to reduce any ϕ to its simplest (in terms of the arithmetical hierarchy) logically equivalent form?

Published on 27 Nov 2012 - 3:59

score 46 · Answer 14 · 2012-11-27 19:28:25

46

Views

Finding polynomials with a specific property

Published on 27 Nov 2012 - 19:28

score 462 · Answer 15 · 2012-11-28 03:39:34

462

Views

I do not understand why the Turing computable sets of N are exactly the sets at level $\Delta_1^0$ of the arithmetical hierarchy

Published on 28 Nov 2012 - 3:39

List Question

Axiomatic system and Hilbert's 2nd problem

Can decidability results for monadic second-order logic be extended to monadic higher-order logics?

are there non-standard models of arithmetic in second order arithmetic?

What is the prerequisite knowledge for learning Godel's incompleteness theorem

Can we prove that a statement cannot be proved?

What does it mean for something to be true but not provable in peano arithmetic?

Provability becoming decidable in a larger system?

Given a φ independent of PA which is true in the standard model, will always (PA+ ¬φ) be ω-inconsistent?

Given a φ independent of PA which is true in the standard model, will always (PA+ ¬φ) be Σn-unsound for some n?

Does Gödel's Incompleteness Theorem really say anything about the limitations of theoretical physics?

What is it wrong in this argument about the interpretability hierarchy?

Is every φ above the second level of the arithmetical hierarchy independent of PA?

Is there a mechanical procedure within PA to reduce any ϕ to its simplest (in terms of the arithmetical hierarchy) logically equivalent form?

Finding polynomials with a specific property

I do not understand why the Turing computable sets of N are exactly the sets at level $\Delta_1^0$ of the arithmetical hierarchy

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