Question

Unprovable sentence, but provably it is provable.

score 209 · Answer 1 · 2026-04-15 14:24:11

209

Views

Unprovable sentence, but provably it is provable.

Published on 15 Apr 2026 - 14:24

score 80 · Answer 2 · 2026-04-12 06:25:04

80

Views

How do Peano's arithmetical axioms guarantee that we can construct the natural number set?

Published on 12 Apr 2026 - 6:25

score 144 · Answer 3 · 2026-05-10 16:11:55

144

Views

Is there a computable and complete "probabilistic" theory of arithmetic?

Published on 10 May 2026 - 16:11

score 460 · Answer 4 · 2026-05-10 14:05:46

460

Views

How do we know PA is incomparable with PRA + $\epsilon_0$?

Published on 10 May 2026 - 14:05

score 59 · Answer 5 · 2026-04-08 23:32:48

59

Views

Basis of Mathematics

Published on 08 Apr 2026 - 23:32

score 348 · Answer 6 · 2026-04-12 06:22:00

348

Views

How can I prove transitivity of < in Peano Arithmetic

Published on 12 Apr 2026 - 6:22

score 111 · Answer 7 · 2026-04-13 04:43:13

111

Views

Must heredity be explicilty stated in addtion to Peano's axioms when defining natural numbers?

Published on 13 Apr 2026 - 4:43

score 74 · Answer 8 · 2026-04-11 17:53:15

74

Views

Why we care only about $\Pi_1$ parameters in axiom schemes?

Published on 11 Apr 2026 - 17:53

score 94 · Answer 9 · 2026-04-12 12:16:35

94

Views

Peano axiom of induction- why cannot it be replaced by something simpler?

Published on 12 Apr 2026 - 12:16

score 125 · Answer 10 · 2026-04-12 11:30:45

125

Views

Peano axioms and first-order logic with $\exists^{\infty}$

Published on 12 Apr 2026 - 11:30

score 37 · Answer 11 · 2026-04-15 18:03:17

37

Views

Are "lower bound" and "upper bound" unambigous? What if one's in the negative axis?

Published on 15 Apr 2026 - 18:03

score 152 · Answer 12 · 2026-04-29 12:19:00

152

Views

Is the 'copy' of the naturals in ZF a unique way to represent the second-order arithmetic in first-order logic?

Published on 29 Apr 2026 - 12:19

score 131 · Answer 13 · 2026-04-16 23:10:09

131

Views

Nonstandard proof codes for Con(PA)

Published on 16 Apr 2026 - 23:10

score 623 · Answer 14 · 2026-05-10 16:13:30

623

Views

How to prove that first-order PA proves the consistency of each of its finite sub-theories?

Published on 10 May 2026 - 16:13

score 141 · Answer 15 · 2026-04-16 21:55:17

141

Views

Peano axioms: prove that there is no natural number between n and sucessor of n

Published on 16 Apr 2026 - 21:55

List Question

Unprovable sentence, but provably it is provable.

How do Peano's arithmetical axioms guarantee that we can construct the natural number set?

Is there a computable and complete "probabilistic" theory of arithmetic?

How do we know PA is incomparable with PRA + $\epsilon_0$?

Basis of Mathematics

How can I prove transitivity of < in Peano Arithmetic

Must heredity be explicilty stated in addtion to Peano's axioms when defining natural numbers?

Why we care only about $\Pi_1$ parameters in axiom schemes?

Peano axiom of induction- why cannot it be replaced by something simpler?

Peano axioms and first-order logic with $\exists^{\infty}$

Are "lower bound" and "upper bound" unambigous? What if one's in the negative axis?

Is the 'copy' of the naturals in ZF a unique way to represent the second-order arithmetic in first-order logic?

Nonstandard proof codes for Con(PA)

How to prove that first-order PA proves the consistency of each of its finite sub-theories?

Peano axioms: prove that there is no natural number between n and sucessor of n

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