Question

Is there a weak set theory that can prove that the natural numbers is a model of PA?

score 146 · Answer 1 · 2026-04-09 02:01:51

146

Views

Is there a weak set theory that can prove that the natural numbers is a model of PA?

Published on 09 Apr 2026 - 2:01

score 283 · Answer 2 · 2026-04-15 06:12:43

283

Views

Why is "$Y = \mathbb{P}(X)$ not a $\Delta_0$?

Published on 15 Apr 2026 - 6:12

score 61 · Answer 3 · 2026-04-14 01:32:53

61

Views

Well ordered uncountable decreasing family with a non zero lower bound

Published on 14 Apr 2026 - 1:32

score 126 · Answer 4 · 2026-04-14 23:36:14

126

Views

$\{ \lambda \in Card | \lambda^k > \lambda\}$ is a proper class

Published on 14 Apr 2026 - 23:36

score 1.1k · Answer 5 · 2026-04-16 15:18:12

1.1k

Views

Proving the Schroeder-Bernstein theorem

Published on 16 Apr 2026 - 15:18

score 34 · Answer 6 · 2026-04-10 06:16:49

34

Views

Are statements allowed to assert something about their containing sets?

Published on 10 Apr 2026 - 6:16

score 50 · Answer 7 · 2026-04-16 04:51:25

50

Views

$j''(X,\mathcal{B})$ being a subspace of $(j(X),j(\mathcal{B}))$ for elementary $j$.

Published on 16 Apr 2026 - 4:51

score 79 · Answer 8 · 2026-04-13 12:56:31

79

Views

If k is a singular cardinal then there is no nonprincipal k-complete ideal over k.

Published on 13 Apr 2026 - 12:56

score 116 · Answer 9 · 2026-04-13 21:17:55

116

Views

Axiom of choice condition.

Published on 13 Apr 2026 - 21:17

score 105 · Answer 10 · 2026-04-09 02:01:48

105

Views

If $G$ is $P$-generic over $V$ and $G^*$ is $j''P$-generic over $M$ then $j$ can be extended to $V[G]$.

Published on 09 Apr 2026 - 2:01

score 32 · Answer 11 · 2026-04-16 09:45:48

32

Views

Exercise IV.17 in Kunen (1980): Absolute in all transitive models of a finite set of ZF axioms implies $\Delta_1$

Published on 16 Apr 2026 - 9:45

score 124 · Answer 12 · 2026-04-14 08:27:42

124

Views

Normality of some generic ultrafilter

Published on 14 Apr 2026 - 8:27

score 87 · Answer 13 · 2026-04-15 16:42:21

87

Views

Connecting models of Set Theory in Jech's text with Model Theory (pages 161-167)

Published on 15 Apr 2026 - 16:42

score 129 · Answer 14 · 2026-04-12 16:59:12

129

Views

Weakest axiom to make ZFC+X imply GCH?

Published on 12 Apr 2026 - 16:59

score 196 · Answer 15 · 2026-04-14 00:26:07

196

Views

how to construct a rudimentary function $h$ used in the paper ''scales in $L(\mathbb{R})$''

Published on 14 Apr 2026 - 0:26

List Question

Is there a weak set theory that can prove that the natural numbers is a model of PA?

Why is "$Y = \mathbb{P}(X)$ not a $\Delta_0$?

Well ordered uncountable decreasing family with a non zero lower bound

$\{ \lambda \in Card | \lambda^k > \lambda\}$ is a proper class

Proving the Schroeder-Bernstein theorem

Are statements allowed to assert something about their containing sets?

$j''(X,\mathcal{B})$ being a subspace of $(j(X),j(\mathcal{B}))$ for elementary $j$.

If k is a singular cardinal then there is no nonprincipal k-complete ideal over k.

Axiom of choice condition.

If $G$ is $P$-generic over $V$ and $G^*$ is $j''P$-generic over $M$ then $j$ can be extended to $V[G]$.

Exercise IV.17 in Kunen (1980): Absolute in all transitive models of a finite set of ZF axioms implies $\Delta_1$

Normality of some generic ultrafilter

Connecting models of Set Theory in Jech's text with Model Theory (pages 161-167)

Weakest axiom to make ZFC+X imply GCH?

how to construct a rudimentary function $h$ used in the paper ''scales in $L(\mathbb{R})$''

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