Question

Prove $\Bbb{N}$ is infinite from Peano axioms

score 197 · Answer 1 · 2026-03-25 03:01:35

197

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Prove $\Bbb{N}$ is infinite from Peano axioms

Published on 25 Mar 2026 - 3:01

score 96 · Answer 2 · 2018-05-01 11:54:58

96

Views

Looking for examples that illustrate the use of the $\operatorname{seq}$ notation

Published on 01 May 2018 - 11:54

score 43 · Answer 3 · 2018-05-06 07:05:05

43

Views

How to prove Peano induction axiom for a candidate model

Published on 06 May 2018 - 7:05

score 1.6k · Answer 4 · 2026-03-25 01:16:45

1.6k

Views

Is it a paradox if I prove something as unprovable?

Published on 25 Mar 2026 - 1:16

score 118 · Answer 5 · 2026-03-22 17:02:41

118

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Systems of arithmetic models

Published on 22 Mar 2026 - 17:02

score 138 · Answer 6 · 2026-03-25 06:09:50

138

Views

ZFC-Infinity+PA: Does it prove Con(PA)?

Published on 25 Mar 2026 - 6:09

score 146 · Answer 7 · 2026-03-25 09:26:22

146

Views

Differences between real numbers in $ACA_0 + \lnot Con(PA)$ and standard real numbers?

Published on 25 Mar 2026 - 9:26

score 323 · Answer 8 · 2018-05-29 00:17:50

323

Views

Can Peano arithmetic prove 0=1 in a standard number of steps (in a non-standard model)?

Published on 29 May 2018 - 0:17

score 527 · Answer 9 · 2026-03-25 01:28:04

527

Views

How can we be so sure that we don't live in Pudlak's inconsistent world?

Published on 25 Mar 2026 - 1:28

score 153 · Answer 10 · 2018-05-30 02:08:16

153

Views

Mathematical Induction and Peano Arithmetic

Published on 30 May 2018 - 2:08

score 181 · Answer 11 · 2026-03-25 01:27:00

181

Views

Can two different models of arithmetic have non-comparable views of peano arithmetic?

Published on 25 Mar 2026 - 1:27

score 521 · Answer 12 · 2018-06-02 01:24:02

521

Views

Can Peano Arithmetic show that the Continuum Hypothesis is Independent of ZFC?

Published on 02 Jun 2018 - 1:24

score 166 · Answer 13 · 2026-03-25 08:58:26

166

Views

Is the famous problem number #6 solvable in first order Peano arithmetic?

Published on 25 Mar 2026 - 8:58

score 210 · Answer 14 · 2026-03-22 05:16:42

210

Views

Can second order peano arithmetic prove that first order peano arithmetic is sound?

Published on 22 Mar 2026 - 5:16

score 100 · Answer 15 · 2018-06-06 21:27:19

100

Views

Can bounded addition and multiplication be computable in a non-standard model of arithmetic?

Published on 06 Jun 2018 - 21:27

List Question

Prove $\Bbb{N}$ is infinite from Peano axioms

Looking for examples that illustrate the use of the $\operatorname{seq}$ notation

How to prove Peano induction axiom for a candidate model

Is it a paradox if I prove something as unprovable?

Systems of arithmetic models

ZFC-Infinity+PA: Does it prove Con(PA)?

Differences between real numbers in $ACA_0 + \lnot Con(PA)$ and standard real numbers?

Can Peano arithmetic prove 0=1 in a standard number of steps (in a non-standard model)?

How can we be so sure that we don't live in Pudlak's inconsistent world?

Mathematical Induction and Peano Arithmetic

Can two different models of arithmetic have non-comparable views of peano arithmetic?

Can Peano Arithmetic show that the Continuum Hypothesis is Independent of ZFC?

Is the famous problem number #6 solvable in first order Peano arithmetic?

Can second order peano arithmetic prove that first order peano arithmetic is sound?

Can bounded addition and multiplication be computable in a non-standard model of arithmetic?

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