Question

What would be the consequences if ZFC proved its own inconsistency, nonconstructively?

score 820 · Answer 1 · 2026-03-26 11:00:17

820

Views

What would be the consequences if ZFC proved its own inconsistency, nonconstructively?

Published on 26 Mar 2026 - 11:00

score 400 · Answer 2 · 2016-07-02 11:09:55

400

Views

I have read that complex axiomatics are Gödel complete, while naturals aren't. Why?

Published on 02 Jul 2016 - 11:09

score 402 · Answer 3 · 2016-07-04 04:13:42

402

Views

Can one have a theory that includes its own consistency as an axiom?

Published on 04 Jul 2016 - 4:13

score 707 · Answer 4 · 2013-04-10 03:08:05

707

Views

Proof of Proposition/Theorem V in Gödel's 1931 paper?

Published on 10 Apr 2013 - 3:08

score 5k · Answer 5 · 2013-04-15 22:16:57

5k

Views

Are Real Numbers axioms a consistent or complete system?

Published on 15 Apr 2013 - 22:16

score 244 · Answer 6 · 2013-04-28 11:11:47

244

Views

If $\operatorname{Con}(\mathrm{PA})$, then $\operatorname{Con}(\mathrm{PA}+\operatorname{Con}(\mathrm{PA}))$?

Published on 28 Apr 2013 - 11:11

score 730 · Answer 7 · 2013-05-01 22:53:54

730

Views

Second order logic question.

Published on 01 May 2013 - 22:53

score 632 · Answer 8 · 2013-05-02 11:17:54

632

Views

Does $\Sigma_1 \cup \Pi_1$ generate the complete first order theory of arithmetic?

Published on 02 May 2013 - 11:17

score 67 · Answer 9 · 2013-05-09 12:03:48

67

Views

Special undecidability situation

Published on 09 May 2013 - 12:03

score 100 · Answer 10 · 2013-05-18 09:56:33

100

Views

Complexity of transforming an indirect proof into a direct one

Published on 18 May 2013 - 9:56

score 275 · Answer 11 · 2013-05-26 18:07:31

275

Views

Gödel's incompleteness wrt weakend versions of ZFC

Published on 26 May 2013 - 18:07

score 644 · Answer 12 · 2013-06-09 18:12:59

644

Views

How is the standard model of number theory specified, and why can't we use that specification to prove any number theoretical sentence of interest?

Published on 09 Jun 2013 - 18:12

score 1.8k · Answer 13 · 2013-06-14 21:16:18

1.8k

Views

Is Gödel's incompleteness theorem provable without any model-theoretic notion?

Published on 14 Jun 2013 - 21:16

score 964 · Answer 14 · 2013-06-23 15:51:20

964

Views

Decidable and recursively-axiomatizable theories

Published on 23 Jun 2013 - 15:51

score 133 · Answer 15 · 2026-03-26 07:59:08

133

Views

Can ZFC+A and ZFC+negation of A be both inconsistent where A is some conjecture?

Published on 26 Mar 2026 - 7:59

List Question

What would be the consequences if ZFC proved its own inconsistency, nonconstructively?

I have read that complex axiomatics are Gödel complete, while naturals aren't. Why?

Can one have a theory that includes its own consistency as an axiom?

Proof of Proposition/Theorem V in Gödel's 1931 paper?

Are Real Numbers axioms a consistent or complete system?

If $\operatorname{Con}(\mathrm{PA})$, then $\operatorname{Con}(\mathrm{PA}+\operatorname{Con}(\mathrm{PA}))$?

Second order logic question.

Does $\Sigma_1 \cup \Pi_1$ generate the complete first order theory of arithmetic?

Special undecidability situation

Complexity of transforming an indirect proof into a direct one

Gödel's incompleteness wrt weakend versions of ZFC

How is the standard model of number theory specified, and why can't we use that specification to prove any number theoretical sentence of interest?

Is Gödel's incompleteness theorem provable without any model-theoretic notion?

Decidable and recursively-axiomatizable theories

Can ZFC+A and ZFC+negation of A be both inconsistent where A is some conjecture?

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