Question

Prove the sum of two natural numbers is again a natural number, using the Peano Axioms.

score 1k · Answer 1 · 2021-07-14 00:56:59

1k

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Prove the sum of two natural numbers is again a natural number, using the Peano Axioms.

Published on 14 Jul 2021 - 0:56

score 66 · Answer 2 · 2021-07-16 22:16:35

66

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Is Peano arithmetic considered to be an algebraic structure?

Published on 16 Jul 2021 - 22:16

score 49 · Answer 3 · 2026-03-26 16:04:17

49

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Can PA prove Cons(PA) under standard model?

Published on 26 Mar 2026 - 16:04

score 58 · Answer 4 · 2021-07-25 03:10:24

58

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For every $a$ in $\mathbb N^+$, prove that there exist a natural number $b$ such that $b++=a$.

Published on 25 Jul 2021 - 3:10

score 68 · Answer 5 · 2026-03-28 10:16:36

68

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Can Peano arithmetic define the set of base 10 palindromic numbers?

Published on 28 Mar 2026 - 10:16

score 206 · Answer 6 · 2026-03-28 07:59:29

206

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What is the definition of the "order" of well order property in Peano Axioms?

Published on 28 Mar 2026 - 7:59

score 86 · Answer 7 · 2026-03-25 22:10:47

86

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Does the degree of impredicativity always matter in type theory?

Published on 25 Mar 2026 - 22:10

score 61 · Answer 8 · 2021-08-04 07:19:58

61

Views

Some questions about the proof of backwards mathematical induction

Published on 04 Aug 2021 - 7:19

score 565 · Answer 9 · 2021-08-06 09:14:11

565

Views

How do I prove there does not exist a natural number $n$ such that $2n=1$ by using Peano's axioms.

Published on 06 Aug 2021 - 9:14

score 120 · Answer 10 · 2021-08-18 22:30:05

120

Views

Does $\mathbb{N}\cup\{\omega\}$ satisfy true arithmetic?

Published on 18 Aug 2021 - 22:30

score 127 · Answer 11 · 2026-03-25 17:20:59

127

Views

Is this an example of the incompleteness of first-order PA?

Published on 25 Mar 2026 - 17:20

score 68 · Answer 12 · 2021-08-31 07:09:06

68

Views

Is the Laws of Form consistent in relation to PA?

Published on 31 Aug 2021 - 7:09

score 131 · Answer 13 · 2026-03-25 17:18:26

131

Views

How does second-order arithmetic rule out non-standard numbers?

Published on 25 Mar 2026 - 17:18

score 136 · Answer 14 · 2021-09-06 16:50:12

136

Views

Does Peano Arithmetic prove all identities involving addition, multiplication, and exponentiation?

Published on 06 Sep 2021 - 16:50

score 836 · Answer 15 · 2026-03-26 17:30:24

836

Views

Incompleteness theorem: Peano arithmetic vs. standard model of arithmetic

Published on 26 Mar 2026 - 17:30

List Question

Prove the sum of two natural numbers is again a natural number, using the Peano Axioms.

Is Peano arithmetic considered to be an algebraic structure?

Can PA prove Cons(PA) under standard model?

For every $a$ in $\mathbb N^+$, prove that there exist a natural number $b$ such that $b++=a$.

Can Peano arithmetic define the set of base 10 palindromic numbers?

What is the definition of the "order" of well order property in Peano Axioms?

Does the degree of impredicativity always matter in type theory?

Some questions about the proof of backwards mathematical induction

How do I prove there does not exist a natural number $n$ such that $2n=1$ by using Peano's axioms.

Does $\mathbb{N}\cup\{\omega\}$ satisfy true arithmetic?

Is this an example of the incompleteness of first-order PA?

Is the Laws of Form consistent in relation to PA?

How does second-order arithmetic rule out non-standard numbers?

Does Peano Arithmetic prove all identities involving addition, multiplication, and exponentiation?

Incompleteness theorem: Peano arithmetic vs. standard model of arithmetic

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