Question

What subsystem of second-order arithmetic proves the weak Godel’s Theorem?

score 60 · Answer 1 · 2026-03-25 18:51:12

60

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What subsystem of second-order arithmetic proves the weak Godel’s Theorem?

Published on 25 Mar 2026 - 18:51

score 173 · Answer 2 · 2026-03-25 14:25:17

173

Views

How to universalize $\text{Prov}(\ulcorner y < K(x)\urcorner) \to y < K(x)$ in a paper of Kikuchi

Published on 25 Mar 2026 - 14:25

score 122 · Answer 3 · 2026-03-25 13:55:25

122

Views

Is there a least standard model of Peano Arithmetics?

Published on 25 Mar 2026 - 13:55

score 249 · Answer 4 · 2026-03-25 17:45:38

249

Views

Formalization in PA in the Kritchman-Raz proof

Published on 25 Mar 2026 - 17:45

score 268 · Answer 5 · 2020-09-17 15:54:22

268

Views

Addition of natural numbers in Edmund Landau's Foundation of Analysis

Published on 17 Sep 2020 - 15:54

score 212 · Answer 6 · 2026-03-25 13:54:06

212

Views

Can theories with axioms beyond arithmetic make false promises about integer existence?

Published on 25 Mar 2026 - 13:54

score 114 · Answer 7 · 2020-09-24 17:03:37

114

Views

Formalizing the number $\#\{n \leq \ell : \varphi(n) \}$ in PA

Published on 24 Sep 2020 - 17:03

score 384 · Answer 8 · 2020-09-27 07:48:00

384

Views

Proof of commutativity of addition using Peano axioms

Published on 27 Sep 2020 - 7:48

score 86 · Answer 9 · 2020-10-06 11:34:26

86

Views

Why are the Peano axioms axioms for natural numbers if they have non-standard models?

Published on 06 Oct 2020 - 11:34

score 147 · Answer 10 · 2020-10-07 05:44:47

147

Views

Can ZFC decide more values of the Busy Beaver function than PA?

Published on 07 Oct 2020 - 5:44

score 753 · Answer 11 · 2026-03-25 13:53:36

753

Views

How can induction work on non-standard natural numbers?

Published on 25 Mar 2026 - 13:53

score 264 · Answer 12 · 2020-10-12 17:34:26

264

Views

Does the well ordering principle really implies mathematical induction?

Published on 12 Oct 2020 - 17:34

score 99 · Answer 13 · 2020-10-13 09:59:30

99

Views

Is Peano Arithmetic the most-commonly used arithmetic system

Published on 13 Oct 2020 - 9:59

score 40 · Answer 14 · 2020-10-21 20:35:57

40

Views

why peano defines 1 as natural?

Published on 21 Oct 2020 - 20:35

score 380 · Answer 15 · 2020-10-22 14:21:26

380

Views

Prove: if $m \in n$ then $m^+ \subseteq n$.

Published on 22 Oct 2020 - 14:21

List Question

What subsystem of second-order arithmetic proves the weak Godel’s Theorem?

How to universalize $\text{Prov}(\ulcorner y < K(x)\urcorner) \to y < K(x)$ in a paper of Kikuchi

Is there a least standard model of Peano Arithmetics?

Formalization in PA in the Kritchman-Raz proof

Addition of natural numbers in Edmund Landau's Foundation of Analysis

Can theories with axioms beyond arithmetic make false promises about integer existence?

Formalizing the number $\#\{n \leq \ell : \varphi(n) \}$ in PA

Proof of commutativity of addition using Peano axioms

Why are the Peano axioms axioms for natural numbers if they have non-standard models?

Can ZFC decide more values of the Busy Beaver function than PA?

How can induction work on non-standard natural numbers?

Does the well ordering principle really implies mathematical induction?

Is Peano Arithmetic the most-commonly used arithmetic system

why peano defines 1 as natural?

Prove: if $m \in n$ then $m^+ \subseteq n$.

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