Question

Examples of statements which are true but not provable

score 7.7k · Answer 1 · 2013-08-15 07:16:41

7.7k

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Examples of statements which are true but not provable

Published on 15 Aug 2013 - 7:16

score 183 · Answer 2 · 2013-08-20 22:52:18

183

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Looking for counterexamples where the output of a computable function always has a computably checkable property, but PA cannot prove this

Published on 20 Aug 2013 - 22:52

score 151 · Answer 3 · 2013-08-22 19:31:15

151

Views

Completeness condition in Gödel first incompleteness theorem superflous

Published on 22 Aug 2013 - 19:31

score 365 · Answer 4 · 2013-08-23 22:57:48

365

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What is the notion of truth used in Godels incompleteness theorem?

Published on 23 Aug 2013 - 22:57

score 159 · Answer 5 · 2013-08-27 00:27:54

159

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Are forcing techniques possible to automate for mechanized reasoning?

Published on 27 Aug 2013 - 0:27

score 695 · Answer 6 · 2013-08-28 13:06:57

695

Views

Problem with completeness theorem and $\mathsf{Con(ZFC)}$

Published on 28 Aug 2013 - 13:06

score 106 · Answer 7 · 2013-09-03 04:41:50

106

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Minimal number of variables in a ZFC-undecidable sentence?

Published on 03 Sep 2013 - 4:41

score 303 · Answer 8 · 2013-09-10 09:40:28

303

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differentiate the terms deductive system, model/structure, formal system, first-order logic

Published on 10 Sep 2013 - 9:40

score 850 · Answer 9 · 2013-09-10 13:41:06

850

Views

clarify the term "arithmetics" when talking about Gödel's incompleteness theorems

Published on 10 Sep 2013 - 13:41

score 72 · Answer 10 · 2013-09-12 11:46:16

72

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Completeness of a Sub Theory of Number Theory

Published on 12 Sep 2013 - 11:46

score 385 · Answer 11 · 2013-09-27 04:19:48

385

Views

Are there complete formal systems?

Published on 27 Sep 2013 - 4:19

score 983 · Answer 12 · 2013-10-07 02:01:27

983

Views

Under the impact of Gödel's incompleteness theorems, are the conclusions of statistics reliable?

Published on 07 Oct 2013 - 2:01

score 459 · Answer 13 · 2013-10-27 14:47:43

459

Views

Is every theorem of PA true in the standard model of number theory $N$?

Published on 27 Oct 2013 - 14:47

score 167 · Answer 14 · 2013-10-27 15:46:40

167

Views

Why does undecidability of arithmetic not follow from that of first-order logic?

Published on 27 Oct 2013 - 15:46

score 197 · Answer 15 · 2013-11-12 08:57:15

197

Views

Impossibility of theories proving consistency of each other?

Published on 12 Nov 2013 - 8:57

List Question

Examples of statements which are true but not provable

Looking for counterexamples where the output of a computable function always has a computably checkable property, but PA cannot prove this

Completeness condition in Gödel first incompleteness theorem superflous

What is the notion of truth used in Godels incompleteness theorem?

Are forcing techniques possible to automate for mechanized reasoning?

Problem with completeness theorem and $\mathsf{Con(ZFC)}$

Minimal number of variables in a ZFC-undecidable sentence?

differentiate the terms deductive system, model/structure, formal system, first-order logic

clarify the term "arithmetics" when talking about Gödel's incompleteness theorems

Completeness of a Sub Theory of Number Theory

Are there complete formal systems?

Under the impact of Gödel's incompleteness theorems, are the conclusions of statistics reliable?

Is every theorem of PA true in the standard model of number theory $N$?

Why does undecidability of arithmetic not follow from that of first-order logic?

Impossibility of theories proving consistency of each other?

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