Question

On an explicit model for $\mathbf Q$ with the negation of the axiom of induction

score 93 · Answer 1 · 2026-03-25 04:42:42

93

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On an explicit model for $\mathbf Q$ with the negation of the axiom of induction

Published on 25 Mar 2026 - 4:42

score 101 · Answer 2 · 2019-11-01 11:21:10

101

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How to show $m+n = n+m$ in the set of Naturals with zero.

Published on 01 Nov 2019 - 11:21

score 185 · Answer 3 · 2026-03-16 13:34:01

185

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What is the smallest ordinal not computable by using artihmetical truth as an oracle?

Published on 16 Mar 2026 - 13:34

score 362 · Answer 4 · 2019-11-12 12:16:55

362

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In Peano arithmetic, can we define inequality using successor?

Published on 12 Nov 2019 - 12:16

score 485 · Answer 5 · 2019-11-18 00:26:06

485

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Help me understand the proof that usual ordering $\leq$ is not first-order definable in the structure $\left(\mathbb{N};s\right)$.

Published on 18 Nov 2019 - 0:26

score 149 · Answer 6 · 2026-03-24 23:54:57

149

Views

Developing model theory in the language of PA

Published on 24 Mar 2026 - 23:54

score 201 · Answer 7 · 2026-03-25 22:10:37

201

Views

What Turing degrees can truth in $\mathbb{N}$ have for different languages?

Published on 25 Mar 2026 - 22:10

score 343 · Answer 8 · 2019-11-20 19:34:06

343

Views

Proof of Edmund Landau's Foundation of Analysis

Published on 20 Nov 2019 - 19:34

score 3.1k · Answer 9 · 2019-11-20 22:06:15

3.1k

Views

How does Peano Postulates construct Natural numbers only?

Published on 20 Nov 2019 - 22:06

score 210 · Answer 10 · 2019-11-22 10:25:43

210

Views

If mathematics has contradictions, will the entire mathematics be destroyed?

Published on 22 Nov 2019 - 10:25

score 146 · Answer 11 · 2019-11-22 17:31:26

146

Views

Am I allowed to substitute terms when reasoning in Peano Arithmetic?

Published on 22 Nov 2019 - 17:31

score 70 · Answer 12 · 2019-11-25 23:20:41

70

Views

Peano Arithmetic and ZFC

Published on 25 Nov 2019 - 23:20

score 111 · Answer 13 · 2026-03-22 04:38:33

111

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What is the omega-completion of $ACA_0$

Published on 22 Mar 2026 - 4:38

score 50 · Answer 14 · 2019-12-01 10:16:24

50

Views

What examples of known theorems of PA that were first provable in stronger set theories like Z or ZFC?

Published on 01 Dec 2019 - 10:16

score 370 · Answer 15 · 2019-12-04 14:08:21

370

Views

Peano axioms without explicit reference to zero

Published on 04 Dec 2019 - 14:08

List Question

On an explicit model for $\mathbf Q$ with the negation of the axiom of induction

How to show $m+n = n+m$ in the set of Naturals with zero.

What is the smallest ordinal not computable by using artihmetical truth as an oracle?

In Peano arithmetic, can we define inequality using successor?

Help me understand the proof that usual ordering $\leq$ is not first-order definable in the structure $\left(\mathbb{N};s\right)$.

Developing model theory in the language of PA

What Turing degrees can truth in $\mathbb{N}$ have for different languages?

Proof of Edmund Landau's Foundation of Analysis

How does Peano Postulates construct Natural numbers only?

If mathematics has contradictions, will the entire mathematics be destroyed?

Am I allowed to substitute terms when reasoning in Peano Arithmetic?

Peano Arithmetic and ZFC

What is the omega-completion of $ACA_0$

What examples of known theorems of PA that were first provable in stronger set theories like Z or ZFC?

Peano axioms without explicit reference to zero

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