Question

What percentage of formulas is unprovable in a given axiomatic system?

score 208 · Answer 1 · 2013-02-20 22:22:40

208

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What percentage of formulas is unprovable in a given axiomatic system?

Published on 20 Feb 2013 - 22:22

score 1.4k · Answer 2 · 2026-03-26 12:32:23

1.4k

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Understanding the syntactical completeness

Published on 26 Mar 2026 - 12:32

score 269 · Answer 3 · 2013-03-18 19:24:29

269

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Talking about Gödel's incompleteness theorems...

Published on 18 Mar 2013 - 19:24

score 307 · Answer 4 · 2026-03-25 08:01:51

307

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How many digits of Chaitin's $\Omega$ constant would we know if we had a $\Sigma_1$-Oracle?

Published on 25 Mar 2026 - 8:01

score 145 · Answer 5 · 2020-07-31 15:15:52

145

Views

Proof of the theorem "Any recursive relation is representable in Cn A$_E$."

Published on 31 Jul 2020 - 15:15

score 353 · Answer 6 · 2020-08-01 03:49:20

353

Views

What is it about natural numbers that makes them a prerequisite for Godel's Incompleteness Theorem to hold?

Published on 01 Aug 2020 - 3:49

score 180 · Answer 7 · 2020-08-01 10:14:27

180

Views

Recursive essentially for Godel incompleteness theorem

Published on 01 Aug 2020 - 10:14

score 929 · Answer 8 · 2020-08-06 20:44:00

929

Views

Does the independence of the axiom of choice imply Gödel's incompleteness theorem?

Published on 06 Aug 2020 - 20:44

score 2k · Answer 9 · 2020-08-13 03:27:55

2k

Views

Is there any metric on R with which it is incomplete.

Published on 13 Aug 2020 - 3:27

score 485 · Answer 10 · 2026-03-26 11:05:24

485

Views

Can inconsistent systems be mathematically interesting/useful?

Published on 26 Mar 2026 - 11:05

score 241 · Answer 11 · 2020-08-25 12:51:50

241

Views

The arithmetized completeness theorem

Published on 25 Aug 2020 - 12:51

score 60 · Answer 12 · 2026-03-25 18:51:12

60

Views

What subsystem of second-order arithmetic proves the weak Godel’s Theorem?

Published on 25 Mar 2026 - 18:51

score 122 · Answer 13 · 2020-08-26 14:28:15

122

Views

Proof of Separation Lemma by Raymond Smullyan in Gödel's Incompleteness Theorems

Published on 26 Aug 2020 - 14:28

score 125 · Answer 14 · 2020-08-27 21:53:41

125

Views

Does Gödel’s theorem preclude the existence of all means of proving all statements in a formal system, or preclude only computable means?

Published on 27 Aug 2020 - 21:53

score 392 · Answer 15 · 2020-08-28 08:22:50

392

Views

Gödel: If a statement of existence is neither provable nor refutable, doesn‘t that imply that the statement is false?

Published on 28 Aug 2020 - 8:22

List Question

What percentage of formulas is unprovable in a given axiomatic system?

Understanding the syntactical completeness

Talking about Gödel's incompleteness theorems...

How many digits of Chaitin's $\Omega$ constant would we know if we had a $\Sigma_1$-Oracle?

Proof of the theorem "Any recursive relation is representable in Cn A$_E$."

What is it about natural numbers that makes them a prerequisite for Godel's Incompleteness Theorem to hold?

Recursive essentially for Godel incompleteness theorem

Does the independence of the axiom of choice imply Gödel's incompleteness theorem?

Is there any metric on R with which it is incomplete.

Can inconsistent systems be mathematically interesting/useful?

The arithmetized completeness theorem

What subsystem of second-order arithmetic proves the weak Godel’s Theorem?

Proof of Separation Lemma by Raymond Smullyan in Gödel's Incompleteness Theorems

Does Gödel’s theorem preclude the existence of all means of proving all statements in a formal system, or preclude only computable means?

Gödel: If a statement of existence is neither provable nor refutable, doesn‘t that imply that the statement is false?

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