Question

Is there a first order formula that is satisfied by $\mathbb{N}$, but not by any other models of Peano axioms?

score 142 · Answer 1 · 2021-06-02 14:11:09

142

Views

Is there a first order formula that is satisfied by $\mathbb{N}$, but not by any other models of Peano axioms?

Published on 02 Jun 2021 - 14:11

score 78 · Answer 2 · 2021-06-04 07:02:34

78

Views

Definition of finite in set theory

Published on 04 Jun 2021 - 7:02

score 44 · Answer 3 · 2021-07-12 10:25:23

44

Views

A non-standard model of PA with total antisymmetric order without induction

Published on 12 Jul 2021 - 10:25

score 126 · Answer 4 · 2021-08-17 13:12:31

126

Views

How would you express, in ZFC, that the number of countable models of Th($\mathbb{N}$), up to isomorphism, is at most $2^{\aleph_0}$?

Published on 17 Aug 2021 - 13:12

score 1k · Answer 5 · 2021-08-29 19:26:45

1k

Views

"Natural" non-standard models of Peano.

Published on 29 Aug 2021 - 19:26

score 126 · Answer 6 · 2021-08-30 16:11:00

126

Views

Is this an example of the incompleteness of first-order PA?

Published on 30 Aug 2021 - 16:11

score 130 · Answer 7 · 2021-08-31 17:30:05

130

Views

How does second-order arithmetic rule out non-standard numbers?

Published on 31 Aug 2021 - 17:30

score 128 · Answer 8 · 2021-09-04 17:25:06

128

Views

Tennenbaum's theorem generalizations: can we have a computable Collatz map on a nonstandard model of Peano?

Published on 04 Sep 2021 - 17:25

score 98 · Answer 9 · 2021-10-25 23:16:13

98

Views

PA├ ∃xP(x) but PA$\nvdash$ P(n) for any n?

Published on 25 Oct 2021 - 23:16

score 72 · Answer 10 · 2021-11-10 04:39:25

72

Views

Enumerating axioms of PA in nonstandard models: trouble in the Kripke-Putnam proof of Gödel's incompleteness theorem

Published on 10 Nov 2021 - 4:39

score 107 · Answer 11 · 2021-11-17 23:34:58

107

Views

Explicitly defining a nonstandard extension of the reals

Published on 17 Nov 2021 - 23:34

score 71 · Answer 12 · 2022-01-12 14:03:51

71

Views

Proving that the Yablo's paradox is $\omega$-inconsistent

Published on 12 Jan 2022 - 14:03

score 233 · Answer 13 · 2022-01-14 03:04:38

233

Views

(Request for) simple constructive proof of existence of nonstandard model of PA

Published on 14 Jan 2022 - 3:04

score 203 · Answer 14 · 2022-02-11 03:41:45

203

Views

Why do we care about PA proving itself consistent?

Published on 11 Feb 2022 - 3:41

score 42 · Answer 15 · 2022-02-21 21:51:51

42

Views

Is $\{\mathcal{B}_T: \mathcal{B}_T$ is isomorphic to $\mathcal{B}_S\}$ countable?

Published on 21 Feb 2022 - 21:51

List Question

Is there a first order formula that is satisfied by $\mathbb{N}$, but not by any other models of Peano axioms?

Definition of finite in set theory

A non-standard model of PA with total antisymmetric order without induction

How would you express, in ZFC, that the number of countable models of Th($\mathbb{N}$), up to isomorphism, is at most $2^{\aleph_0}$?

"Natural" non-standard models of Peano.

Is this an example of the incompleteness of first-order PA?

How does second-order arithmetic rule out non-standard numbers?

Tennenbaum's theorem generalizations: can we have a computable Collatz map on a nonstandard model of Peano?

PA├ ∃xP(x) but PA$\nvdash$ P(n) for any n?

Enumerating axioms of PA in nonstandard models: trouble in the Kripke-Putnam proof of Gödel's incompleteness theorem

Explicitly defining a nonstandard extension of the reals

Proving that the Yablo's paradox is $\omega$-inconsistent

(Request for) simple constructive proof of existence of nonstandard model of PA

Why do we care about PA proving itself consistent?

Is $\{\mathcal{B}_T: \mathcal{B}_T$ is isomorphic to $\mathcal{B}_S\}$ countable?

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