Question

Is there a problem if I don't use $0$ in Peano arithmetic?

score 67 · Answer 1 · 2024-03-22 23:37:27

67

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Is there a problem if I don't use $0$ in Peano arithmetic?

Published on 22 Mar 2024 - 23:37

score 68 · Answer 2 · 2024-03-23 07:31:10

68

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Is it possible to construct a real number theory on Peano arithmetic?

Published on 23 Mar 2024 - 7:31

score 137 · Answer 3 · 2024-03-23 13:19:53

137

Views

An example of a subset of $\mathbb{N}$ that is used in number theory but cannot be written in terms of Peano arithmetic.

Published on 23 Mar 2024 - 13:19

score 57 · Answer 4 · 2026-03-25 13:54:14

57

Views

Why doesn't $RCA_0$ prove $\Sigma^0_1$-comprehension?

Published on 25 Mar 2026 - 13:54

score 110 · Answer 5 · 2024-03-26 16:10:37

110

Views

Understanding the Arithmetical Hierarchy

Published on 26 Mar 2024 - 16:10

score 121 · Answer 6 · 2026-03-26 01:14:45

121

Views

Is Gödels second incompleteness theorem provable within peano arithmetic?

Published on 26 Mar 2026 - 1:14

score 72 · Answer 7 · 2024-03-31 15:51:28

72

Views

Can ZFC define every function and relation that PA can define, plus more?

Published on 31 Mar 2024 - 15:51

score 133 · Answer 8 · 2026-03-26 03:01:45

133

Views

For which subsystems T of 2nd order arithmetic is there a model of T + $\neg$Con(T)?

Published on 26 Mar 2026 - 3:01

score 170 · Answer 9 · 2015-01-04 23:04:43

170

Views

Why isn't it necessary to postulate the existence of $1$?

Published on 04 Jan 2015 - 23:04

score 256 · Answer 10 · 2015-01-06 02:41:45

256

Views

Reference request - Outline of Edward Nelson's Inconsistency Proof

Published on 06 Jan 2015 - 2:41

score 895 · Answer 11 · 2026-03-27 01:43:42

895

Views

Why are all computable functions representable in PA?

Published on 27 Mar 2026 - 1:43

score 859 · Answer 12 · 2015-01-10 11:50:48

859

Views

Another problem on Peano Axioms (indirectly) from Tao's Analysis book

Published on 10 Jan 2015 - 11:50

score 4.7k · Answer 13 · 2015-01-18 19:03:17

4.7k

Views

Why don't we use Presburger's arithmetic instead of Peano's arithmetic?

Published on 18 Jan 2015 - 19:03

score 234 · Answer 14 · 2015-01-22 23:20:36

234

Views

Possible not countable extension of the natural numbers?

Published on 22 Jan 2015 - 23:20

score 306 · Answer 15 · 2015-01-25 01:57:08

306

Views

Why is it impossible to define multiplication in Presburger arithmetic yet possible to define exponentiation in Peano Arithmethic?

Published on 25 Jan 2015 - 1:57

List Question

Is there a problem if I don't use $0$ in Peano arithmetic?

Is it possible to construct a real number theory on Peano arithmetic?

An example of a subset of $\mathbb{N}$ that is used in number theory but cannot be written in terms of Peano arithmetic.

Why doesn't $RCA_0$ prove $\Sigma^0_1$-comprehension?

Understanding the Arithmetical Hierarchy

Is Gödels second incompleteness theorem provable within peano arithmetic?

Can ZFC define every function and relation that PA can define, plus more?

For which subsystems T of 2nd order arithmetic is there a model of T + $\neg$Con(T)?

Why isn't it necessary to postulate the existence of $1$?

Reference request - Outline of Edward Nelson's Inconsistency Proof

Why are all computable functions representable in PA?

Another problem on Peano Axioms (indirectly) from Tao's Analysis book

Why don't we use Presburger's arithmetic instead of Peano's arithmetic?

Possible not countable extension of the natural numbers?

Why is it impossible to define multiplication in Presburger arithmetic yet possible to define exponentiation in Peano Arithmethic?

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