Question

Show that there are only $\aleph_0$ many countable models of the following theory.

score 118 · Answer 1 · 2017-10-03 10:14:22

118

Views

Show that there are only $\aleph_0$ many countable models of the following theory.

Published on 03 Oct 2017 - 10:14

score 78 · Answer 2 · 2017-10-10 08:34:36

78

Views

Clarification needed on ordering $\mathbb{Z}[X]$ in the language of arithmetic.

Published on 10 Oct 2017 - 8:34

score 72 · Answer 3 · 2017-10-11 05:19:48

72

Views

Upper bound of the "number" of countable models of Th$\mathbb{N}$ up to isomorphism

Published on 11 Oct 2017 - 5:19

score 246 · Answer 4 · 2017-10-20 14:05:48

246

Views

Why do we need second-order logic?

Published on 20 Oct 2017 - 14:05

score 870 · Answer 5 · 2017-10-21 05:04:06

870

Views

Precise reason why a non standard model of arithmetic is not isomorphic to the natural numbers

Published on 21 Oct 2017 - 5:04

score 514 · Answer 6 · 2017-10-28 20:25:09

514

Views

Formulation of the Successor Function as an Endofunction in First-Order Logic

Published on 28 Oct 2017 - 20:25

score 143 · Answer 7 · 2017-11-10 09:04:59

143

Views

Why the following initial segment is NOT a model of PA

Published on 10 Nov 2017 - 9:04

score 1.3k · Answer 8 · 2017-11-11 20:32:38

1.3k

Views

Who first proved Peano Arithmetic is not finitely axiomatizable?

Published on 11 Nov 2017 - 20:32

score 117 · Answer 9 · 2017-11-16 05:59:43

117

Views

What's a good source on how to construct all sets of numbers?

Published on 16 Nov 2017 - 5:59

score 87 · Answer 10 · 2017-11-21 07:24:32

87

Views

Logic proof for $(x\leq y\to 0\leq y-x), x+y-y=x$, and the property that the product two consecutive numbers is even

Published on 21 Nov 2017 - 7:24

score 983 · Answer 11 · 2017-11-21 13:34:33

983

Views

Proving that no number is the successor of itself

Published on 21 Nov 2017 - 13:34

score 132 · Answer 12 · 2017-12-05 19:32:03

132

Views

For any two models of PA, is one model a cut of the other?

Published on 05 Dec 2017 - 19:32

score 1.2k · Answer 13 · 2026-03-26 02:55:00

1.2k

Views

Is every true statement about the natural numbers provable in ZFC?

Published on 26 Mar 2026 - 2:55

score 1.6k · Answer 14 · 2010-08-29 18:24:10

1.6k

Views

Is there a natural model of Peano Arithmetic where Goodstein's theorem fails?

Published on 29 Aug 2010 - 18:24

score 10k · Answer 15 · 2011-01-07 12:17:16

10k

Views

Why is Peano arithmetic undecidable?

Published on 07 Jan 2011 - 12:17

List Question

Show that there are only $\aleph_0$ many countable models of the following theory.

Clarification needed on ordering $\mathbb{Z}[X]$ in the language of arithmetic.

Upper bound of the "number" of countable models of Th$\mathbb{N}$ up to isomorphism

Why do we need second-order logic?

Precise reason why a non standard model of arithmetic is not isomorphic to the natural numbers

Formulation of the Successor Function as an Endofunction in First-Order Logic

Why the following initial segment is NOT a model of PA

Who first proved Peano Arithmetic is not finitely axiomatizable?

What's a good source on how to construct all sets of numbers?

Logic proof for $(x\leq y\to 0\leq y-x), x+y-y=x$, and the property that the product two consecutive numbers is even

Proving that no number is the successor of itself

For any two models of PA, is one model a cut of the other?

Is every true statement about the natural numbers provable in ZFC?

Is there a natural model of Peano Arithmetic where Goodstein's theorem fails?

Why is Peano arithmetic undecidable?

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