Question

First Incompleteness Theorem: Does the limit of $\mathsf{T}_n\cup\{\rho_{\mathsf{T}_n}\}$ exist?

score 167 · Answer 1 · 2016-03-18 19:30:36

167

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First Incompleteness Theorem: Does the limit of $\mathsf{T}_n\cup\{\rho_{\mathsf{T}_n}\}$ exist?

Published on 18 Mar 2016 - 19:30

score 46 · Answer 2 · 2016-03-31 01:23:19

46

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Same number of provable as unprovable statements?

Published on 31 Mar 2016 - 1:23

score 141 · Answer 3 · 2016-04-08 15:22:27

141

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Exercise Henkin Theory

Published on 08 Apr 2016 - 15:22

score 249 · Answer 4 · 2026-03-25 17:39:43

249

Views

What is the simplest formal system falling prey to Gödel's incompleteness theorems?

Published on 25 Mar 2026 - 17:39

score 72 · Answer 5 · 2026-03-25 19:05:24

72

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Any foundational theory of math falls prey to the incompleteness theorems - true or false?

Published on 25 Mar 2026 - 19:05

score 47 · Answer 6 · 2016-04-14 22:37:52

47

Views

Can we prove undefinability theorem first (using techniques that are different from Godel's) and then deduce Incompleteness from it?

Published on 14 Apr 2016 - 22:37

score 161 · Answer 7 · 2016-04-15 07:10:11

161

Views

Impossibility of proving a foundation to be consistent

Published on 15 Apr 2016 - 7:10

score 87 · Answer 8 · 2016-04-17 07:38:44

87

Views

Can there be true but unprovable statements about object other than numbers?

Published on 17 Apr 2016 - 7:38

score 399 · Answer 9 · 2026-03-25 19:01:15

399

Views

Why can't we keep adding axioms forever?

Published on 25 Mar 2026 - 19:01

score 97 · Answer 10 · 2016-05-13 06:15:12

97

Views

Minimal arithmetic proving a statement similar to a Gödel sentence

Published on 13 May 2016 - 6:15

score 279 · Answer 11 · 2026-03-26 11:03:17

279

Views

If a theory is 1-consistent then it is consistent

Published on 26 Mar 2026 - 11:03

score 264 · Answer 12 · 2026-03-26 06:19:15

264

Views

Busy Beaver unprovoable for large inputs?

Published on 26 Mar 2026 - 6:19

score 246 · Answer 13 · 2016-05-18 09:01:14

246

Views

Is ZFC ω-consistent over ZF?

Published on 18 May 2016 - 9:01

score 915 · Answer 14 · 2016-06-12 16:41:59

915

Views

Are Godel's incompleteness theorems proven non-trivial?

Published on 12 Jun 2016 - 16:41

score 609 · Answer 15 · 2026-03-26 06:21:45

609

Views

Why is the proof of Gödel's first incompleteness theorem no contradiction?

Published on 26 Mar 2026 - 6:21

List Question

First Incompleteness Theorem: Does the limit of $\mathsf{T}_n\cup\{\rho_{\mathsf{T}_n}\}$ exist?

Same number of provable as unprovable statements?

Exercise Henkin Theory

What is the simplest formal system falling prey to Gödel's incompleteness theorems?

Any foundational theory of math falls prey to the incompleteness theorems - true or false?

Can we prove undefinability theorem first (using techniques that are different from Godel's) and then deduce Incompleteness from it?

Impossibility of proving a foundation to be consistent

Can there be true but unprovable statements about object other than numbers?

Why can't we keep adding axioms forever?

Minimal arithmetic proving a statement similar to a Gödel sentence

If a theory is 1-consistent then it is consistent

Busy Beaver unprovoable for large inputs?

Is ZFC ω-consistent over ZF?

Are Godel's incompleteness theorems proven non-trivial?

Why is the proof of Gödel's first incompleteness theorem no contradiction?

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