Question

is arithmetic finitely consistent?

score 109 · Answer 1 · 2026-03-27 00:01:39

109

Views

is arithmetic finitely consistent?

Published on 27 Mar 2026 - 0:01

score 139 · Answer 2 · 2026-03-27 00:02:20

139

Views

Infinite statements from finite axioms

Published on 27 Mar 2026 - 0:02

score 96 · Answer 3 · 2026-03-27 00:02:20

96

Views

Confusion about $\mathsf{PA}$'s self-provable consistency sentences

Published on 27 Mar 2026 - 0:02

score 238 · Answer 4 · 2026-03-25 12:54:38

238

Views

Why Löwenheim–Skolem theorem asserts the non-existence of such predicates in 1st order logic

Published on 25 Mar 2026 - 12:54

score 94 · Answer 5 · 2024-02-18 16:34:51

94

Views

Model Theory in the Language of Peano Arithmetic

Published on 18 Feb 2024 - 16:34

score 185 · Answer 6 · 2024-02-26 21:54:18

185

Views

Do $P(0)$ and $P(n)\implies P(n+1)$ yield $P(5)$ without an axiom of induction?

Published on 26 Feb 2024 - 21:54

score 91 · Answer 7 · 2026-03-25 12:49:47

91

Views

In the axiomatic treatment of natural numbers, can we define what a natural number is?

Published on 25 Mar 2026 - 12:49

score 159 · Answer 8 · 2026-03-27 00:02:47

159

Views

Precise statement of Gödel's Incompleteness Theorems

Published on 27 Mar 2026 - 0:02

score 73 · Answer 9 · 2024-03-13 20:50:25

73

Views

Rigorous proof that cardinality of a disjoint union is the sum of cardinalities for finite sets

Published on 13 Mar 2024 - 20:50

score 98 · Answer 10 · 2024-03-13 22:01:51

98

Views

Proving the Weak Goodstein Theorem within $\mathsf{PA}$

Published on 13 Mar 2024 - 22:01

score 76 · Answer 11 · 2024-03-14 02:31:46

76

Views

Can we conclude that Peano's axioms consistent from soundness?

Published on 14 Mar 2024 - 2:31

score 87 · Answer 12 · 2024-03-14 13:48:20

87

Views

Help me check my proof of the cancellation law for natural numbers (without trichotomy)

Published on 14 Mar 2024 - 13:48

score 405 · Answer 13 · 2026-03-27 00:10:38

405

Views

PA + "(PA + this axiom) is consistent"

Published on 27 Mar 2026 - 0:10

score 125 · Answer 14 · 2024-03-17 22:59:16

125

Views

Does self-reference make the Peano-Russell system inconsistent?

Published on 17 Mar 2024 - 22:59

score 206 · Answer 15 · 2024-03-22 17:19:51

206

Views

Allegedly: the existence of a natural number and successors does not imply, without the Axiom of Infinity, the existence of an infinite set.

Published on 22 Mar 2024 - 17:19

List Question

is arithmetic finitely consistent?

Infinite statements from finite axioms

Confusion about $\mathsf{PA}$'s self-provable consistency sentences

Why Löwenheim–Skolem theorem asserts the non-existence of such predicates in 1st order logic

Model Theory in the Language of Peano Arithmetic

Do $P(0)$ and $P(n)\implies P(n+1)$ yield $P(5)$ without an axiom of induction?

In the axiomatic treatment of natural numbers, can we define what a natural number is?

Precise statement of Gödel's Incompleteness Theorems

Rigorous proof that cardinality of a disjoint union is the sum of cardinalities for finite sets

Proving the Weak Goodstein Theorem within $\mathsf{PA}$

Can we conclude that Peano's axioms consistent from soundness?

Help me check my proof of the cancellation law for natural numbers (without trichotomy)

PA + "(PA + this axiom) is consistent"

Does self-reference make the Peano-Russell system inconsistent?

Allegedly: the existence of a natural number and successors does not imply, without the Axiom of Infinity, the existence of an infinite set.

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