Question

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

score 90 · Answer 1 · 2026-04-13 16:50:41

90

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

Published on 13 Apr 2026 - 16:50

score 7.2k · Answer 2 · 2026-04-10 15:55:41

7.2k

Views

Why does induction have to be an axiom?

Published on 10 Apr 2026 - 15:55

score 912 · Answer 3 · 2026-04-09 20:02:44

912

Views

Does the successor function imply order?

Published on 09 Apr 2026 - 20:02

score 88 · Answer 4 · 2026-04-14 12:53:30

88

Views

Peano axioms and Herbrand's theorem

Published on 14 Apr 2026 - 12:53

score 77 · Answer 5 · 2026-04-15 14:47:49

77

Views

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

Published on 15 Apr 2026 - 14:47

score 153 · Answer 6 · 2026-04-14 16:22:09

153

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 14 Apr 2026 - 16:22

score 1k · Answer 7 · 2026-04-14 09:59:35

1k

Views

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

Published on 14 Apr 2026 - 9:59

score 78 · Answer 8 · 2026-04-14 22:58:31

78

Views

Deciding whether sets of Godel's number is recursive.

Published on 14 Apr 2026 - 22:58

score 798 · Answer 9 · 2026-04-12 10:26:01

798

Views

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

Published on 12 Apr 2026 - 10:26

score 1.5k · Answer 10 · 2026-04-15 00:00:29

1.5k

Views

Order of the natural numbers

Published on 15 Apr 2026 - 0:00

score 197 · Answer 11 · 2026-05-10 12:31:50

197

Views

Proof predicate in PA and stronger system

Published on 10 May 2026 - 12:31

score 51 · Answer 12 · 2026-05-10 12:32:24

51

Views

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

Published on 10 May 2026 - 12:32

score 858 · Answer 13 · 2026-04-12 18:33:53

858

Views

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

Published on 12 Apr 2026 - 18:33

score 757 · Answer 14 · 2026-04-16 03:09:32

757

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 16 Apr 2026 - 3:09

score 95 · Answer 15 · 2026-05-10 16:00:52

95

Views

Research areas in Peano arithmetics

Published on 10 May 2026 - 16:00

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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