Question

Proof that an injective system with $i\notin\textrm{ran}{f}$ has a Peano subsystem.

score 88 · Answer 1 · 2026-03-25 06:03:20

88

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Proof that an injective system with $i\notin\textrm{ran}{f}$ has a Peano subsystem.

Published on 25 Mar 2026 - 6:03

score 7.2k · Answer 2 · 2026-03-25 07:41:59

7.2k

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Why does induction have to be an axiom?

Published on 25 Mar 2026 - 7:41

score 908 · Answer 3 · 2018-06-17 18:27:15

908

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Does the successor function imply order?

Published on 17 Jun 2018 - 18:27

score 85 · Answer 4 · 2018-06-19 11:54:19

85

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Peano axioms and Herbrand's theorem

Published on 19 Jun 2018 - 11:54

score 74 · Answer 5 · 2018-06-29 17:23:17

74

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$PA \vdash \forall x(S(S(S...(S(x))...))) \neq \bar{0} $

Published on 29 Jun 2018 - 17:23

score 151 · Answer 6 · 2018-07-03 03:37:11

151

Views

$\forall k,n \in\mathbb N:k\in n\iff k\subsetneq n$ [Proof Verification and Suggestion for shorter or simpler proof]

Published on 03 Jul 2018 - 3:37

score 1k · Answer 7 · 2018-07-07 11:54:58

1k

Views

"No infinite descending membership chains", Peano Axioms, Axiom of Regularity

Published on 07 Jul 2018 - 11:54

score 75 · Answer 8 · 2018-07-08 08:48:57

75

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Deciding whether sets of Godel's number is recursive.

Published on 08 Jul 2018 - 8:48

score 796 · Answer 9 · 2026-03-25 04:37:59

796

Views

Does countable induction over $\mathbb N$ require the axiom of infinity?

Published on 25 Mar 2026 - 4:37

score 1.5k · Answer 10 · 2018-07-17 15:11:07

1.5k

Views

Order of the natural numbers

Published on 17 Jul 2018 - 15:11

score 191 · Answer 11 · 2026-03-25 04:36:36

191

Views

Proof predicate in PA and stronger system

Published on 25 Mar 2026 - 4:36

score 46 · Answer 12 · 2026-03-25 06:00:19

46

Views

Would a proof predicate change if a stronger system used despite sharing language?

Published on 25 Mar 2026 - 6:00

score 855 · Answer 13 · 2018-07-28 07:42:31

855

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How to prove the generalized associative law for addition on $\mathbb N$?

Published on 28 Jul 2018 - 7:42

score 755 · Answer 14 · 2026-03-25 09:43:08

755

Views

How can I prove this proposition from Peano Axioms: (Cancellation law). Let a, b, c be natural numbers such that a + b = a + c. Then we have b = c.

Published on 25 Mar 2026 - 9:43

score 92 · Answer 15 · 2026-03-25 01:22:24

92

Views

Research areas in Peano arithmetics

Published on 25 Mar 2026 - 1:22

List Question

Proof that an injective system with $i\notin\textrm{ran}{f}$ has a Peano subsystem.

Why does induction have to be an axiom?

Does the successor function imply order?

Peano axioms and Herbrand's theorem

$PA \vdash \forall x(S(S(S...(S(x))...))) \neq \bar{0} $

$\forall k,n \in\mathbb N:k\in n\iff k\subsetneq n$ [Proof Verification and Suggestion for shorter or simpler proof]

"No infinite descending membership chains", Peano Axioms, Axiom of Regularity

Deciding whether sets of Godel's number is recursive.

Does countable induction over $\mathbb N$ require the axiom of infinity?

Order of the natural numbers

Proof predicate in PA and stronger system

Would a proof predicate change if a stronger system used despite sharing language?

How to prove the generalized associative law for addition on $\mathbb N$?

How can I prove this proposition from Peano Axioms: (Cancellation law). Let a, b, c be natural numbers such that a + b = a + c. Then we have b = c.

Research areas in Peano arithmetics

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