Question

Do Gödel's incompleteness theorems apply to finitist axiomatic systems that reject the axiom of infinity?

score 222 · Answer 1 · 2026-03-25 23:11:02

222

Views

Do Gödel's incompleteness theorems apply to finitist axiomatic systems that reject the axiom of infinity?

Published on 25 Mar 2026 - 23:11

score 433 · Answer 2 · 2026-03-16 21:32:04

433

Views

Are there "interesting" theorems in Peano arithmetic, that only use the addition operation?

Published on 16 Mar 2026 - 21:32

score 1.1k · Answer 3 · 2019-05-09 01:13:36

1.1k

Views

Proof of cancellation law for multiplication of natural numbers.

Published on 09 May 2019 - 1:13

score 79 · Answer 4 · 2019-05-10 14:42:00

79

Views

Terminology: arithmetic vs. expressible vs. represented

Published on 10 May 2019 - 14:42

score 86 · Answer 5 · 2019-05-13 13:25:29

86

Views

Peano axioms: S(1)=1?

Published on 13 May 2019 - 13:25

score 82 · Answer 6 · 2019-05-15 04:17:14

82

Views

Is Peano's axiom of induction needed to show $n^\prime\ne n^{\prime\prime}$?

Published on 15 May 2019 - 4:17

score 67 · Answer 7 · 2026-03-25 21:51:16

67

Views

Does $n^\prime\ne n^{\prime\prime}$ require proof by contradiction? $n^\prime$ is the successor of $n$.

Published on 25 Mar 2026 - 21:51

score 89 · Answer 8 · 2019-05-21 11:39:48

89

Views

Is there an error in this proof the the "strong induction" theorem? Is this Escherian logic?

Published on 21 May 2019 - 11:39

score 87 · Answer 9 · 2019-06-09 16:30:33

87

Views

Taking a natural number different from zero as a base case in an inductive proof

Published on 09 Jun 2019 - 16:30

score 209 · Answer 10 · 2019-06-10 10:05:51

209

Views

Proof that Peano Axioms is a theory with equality (according to Mendelson book)

Published on 10 Jun 2019 - 10:05

score 132 · Answer 11 · 2019-06-13 08:11:38

132

Views

(Peano axioms) Showing why the induction axiom is necessary

Published on 13 Jun 2019 - 8:11

score 417 · Answer 12 · 2019-06-17 19:20:18

417

Views

Why does induction only allow numbers connected to $0$ to be natural?

Published on 17 Jun 2019 - 19:20

score 163 · Answer 13 · 2019-06-22 19:34:57

163

Views

I am confused about how we should state the Peano axioms

Published on 22 Jun 2019 - 19:34

score 118 · Answer 14 · 2019-06-23 08:12:17

118

Views

Proof of σ(m) + n = m + σ(n)

Published on 23 Jun 2019 - 8:12

score 208 · Answer 15 · 2019-06-24 19:49:05

208

Views

Requirements for claiming Con(PA) is true

Published on 24 Jun 2019 - 19:49

List Question

Do Gödel's incompleteness theorems apply to finitist axiomatic systems that reject the axiom of infinity?

Are there "interesting" theorems in Peano arithmetic, that only use the addition operation?

Proof of cancellation law for multiplication of natural numbers.

Terminology: arithmetic vs. expressible vs. represented

Peano axioms: S(1)=1?

Is Peano's axiom of induction needed to show $n^\prime\ne n^{\prime\prime}$?

Does $n^\prime\ne n^{\prime\prime}$ require proof by contradiction? $n^\prime$ is the successor of $n$.

Is there an error in this proof the the "strong induction" theorem? Is this Escherian logic?

Taking a natural number different from zero as a base case in an inductive proof

Proof that Peano Axioms is a theory with equality (according to Mendelson book)

(Peano axioms) Showing why the induction axiom is necessary

Why does induction only allow numbers connected to $0$ to be natural?

I am confused about how we should state the Peano axioms

Proof of σ(m) + n = m + σ(n)

Requirements for claiming Con(PA) is true

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