Question

Existence of a structure with the same properties as $\mathbb{N}$ and with an infinite element.

score 81 · Answer 1 · 2026-03-17 09:17:04

81

Views

Existence of a structure with the same properties as $\mathbb{N}$ and with an infinite element.

Published on 17 Mar 2026 - 9:17

score 722 · Answer 2 · 2026-03-17 16:59:49

722

Views

Non-standard model of arithmetic - why is adding new constants to the model acceptable?

Published on 17 Mar 2026 - 16:59

score 146 · Answer 3 · 2026-03-23 04:03:43

146

Views

Any non-standard halting oracles stronger than $\mathbb N$?

Published on 23 Mar 2026 - 4:03

score 103 · Answer 4 · 2026-03-16 23:37:42

103

Views

Having Trouble Seeing Why Friedman's Theorem (1973) is true.

Published on 16 Mar 2026 - 23:37

score 506 · Answer 5 · 2026-03-17 08:20:35

506

Views

Non-standard integers?

Published on 17 Mar 2026 - 8:20

score 110 · Answer 6 · 2026-03-17 18:07:34

110

Views

Is there a combined theory of the Reals and the Naturals that has a model where the Naturals and Reals have the same cardinality

Published on 17 Mar 2026 - 18:07

score 68 · Answer 7 · 2026-03-17 05:43:59

68

Views

Is the union of non-standard analogs of a family of sets a proper subset of the non-standard analog of the union of those sets?

Published on 17 Mar 2026 - 5:43

score 436 · Answer 8 · 2026-03-17 20:44:02

436

Views

The satisfaction relation is undefinable, but does it still "exist"?

Published on 17 Mar 2026 - 20:44

score 246 · Answer 9 · 2026-03-17 02:26:34

246

Views

Is the standard model for the language of number theory elementarily equivalent to one with a nonstandard element?

Published on 17 Mar 2026 - 2:26

score 260 · Answer 10 · 2026-03-17 16:07:34

260

Views

Exponentiation and a weak fragment of arithmetic

Published on 17 Mar 2026 - 16:07

score 81 · Answer 11 · 2026-03-17 02:54:54

81

Views

Generalizing the construction of $PA^\omega$

Published on 17 Mar 2026 - 2:54

score 271 · Answer 12 · 2026-03-17 20:31:52

271

Views

Elementary equivalence of standard and non-standard model of arithmetic

Published on 17 Mar 2026 - 20:31

score 61 · Answer 13 · 2026-03-17 02:39:05

61

Views

Internal Set Theory: Start with nonstandard finite E, then the standard subset of E is infinite?

Published on 17 Mar 2026 - 2:39

score 79 · Answer 14 · 2026-03-17 05:25:46

79

Views

Internal Set Theory: extensionality (set equality)

Published on 17 Mar 2026 - 5:25

score 124 · Answer 15 · 2026-03-16 22:16:12

124

Views

First-order Peano arithmetic and (the lack of) implicit definition of addition

Published on 16 Mar 2026 - 22:16

List Question

Existence of a structure with the same properties as $\mathbb{N}$ and with an infinite element.

Non-standard model of arithmetic - why is adding new constants to the model acceptable?

Any non-standard halting oracles stronger than $\mathbb N$?

Having Trouble Seeing Why Friedman's Theorem (1973) is true.

Non-standard integers?

Is there a combined theory of the Reals and the Naturals that has a model where the Naturals and Reals have the same cardinality

Is the union of non-standard analogs of a family of sets a proper subset of the non-standard analog of the union of those sets?

The satisfaction relation is undefinable, but does it still "exist"?

Is the standard model for the language of number theory elementarily equivalent to one with a nonstandard element?

Exponentiation and a weak fragment of arithmetic

Generalizing the construction of $PA^\omega$

Elementary equivalence of standard and non-standard model of arithmetic

Internal Set Theory: Start with nonstandard finite E, then the standard subset of E is infinite?

Internal Set Theory: extensionality (set equality)

First-order Peano arithmetic and (the lack of) implicit definition of addition

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