Question

How can I prove that primitive recursion "preserves" representability in Peano Arithmetic?

score 76 · Answer 1 · 2026-03-26 12:53:16

76

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How can I prove that primitive recursion "preserves" representability in Peano Arithmetic?

Published on 26 Mar 2026 - 12:53

score 35 · Answer 2 · 2020-10-08 13:55:18

35

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Prove that there are exists two denumerable sets $A and B$ such that ${ab| a \in A, b \in B}$ is enumerable.

Published on 08 Oct 2020 - 13:55

score 59 · Answer 3 · 2020-10-12 17:38:24

59

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What mistake am I making interpreting this proposition related to the Recursion Theorem?

Published on 12 Oct 2020 - 17:38

score 44 · Answer 4 · 2020-10-15 12:52:31

44

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Every computational task can be solved with $O(1)$ additional memory

Published on 15 Oct 2020 - 12:52

score 606 · Answer 5 · 2026-03-29 14:57:45

606

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An arbitatry subset of a Turing-recognizable language, is also a Turing-recognizable language?

Published on 29 Mar 2026 - 14:57

score 298 · Answer 6 · 2026-04-01 04:59:38

298

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A computably enumerable set $m$-reduces to the halting problem

Published on 01 Apr 2026 - 4:59

score 109 · Answer 7 · 2026-03-29 15:02:25

109

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Does there exist an Ordinal Turing Machine program which can detect the occurrence of accidentally writable reals on the tape of a simulated program?

Published on 29 Mar 2026 - 15:02

score 556 · Answer 8 · 2026-02-23 21:15:15

556

Views

Boolos’s proof of Gödel’s first incompleteness theorem. What am I getting wrong?

Published on 23 Feb 2026 - 21:15

score 140 · Answer 9 · 2020-10-20 00:08:27

140

Views

How will Mathematics courses help learning Computability Theory and Complexity Theory?

Published on 20 Oct 2020 - 0:08

score 178 · Answer 10 · 2020-10-20 13:07:54

178

Views

On Shoenfield's Mathematical Logic, Chapter 6 Q2

Published on 20 Oct 2020 - 13:07

score 62 · Answer 11 · 2020-10-22 02:33:15

62

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Sets which are strictly $\Sigma_n$ but not $\Sigma_n$-complete

Published on 22 Oct 2020 - 2:33

score 150 · Answer 12 · 2020-10-23 11:39:51

150

Views

Is this problem computable?

Published on 23 Oct 2020 - 11:39

score 39 · Answer 13 · 2020-10-23 18:49:06

39

Views

Showing that the diagonal set is $\Pi_k$

Published on 23 Oct 2020 - 18:49

score 153 · Answer 14 · 2020-10-23 23:32:14

153

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Bounded quantifiers don't count in arithmetic hierarchy

Published on 23 Oct 2020 - 23:32

score 125 · Answer 15 · 2020-10-24 19:29:42

125

Views

Proving equality of functions defined by primitive recursion

Published on 24 Oct 2020 - 19:29

List Question

How can I prove that primitive recursion "preserves" representability in Peano Arithmetic?

Prove that there are exists two denumerable sets $A and B$ such that ${ab| a \in A, b \in B}$ is enumerable.

What mistake am I making interpreting this proposition related to the Recursion Theorem?

Every computational task can be solved with $O(1)$ additional memory

An arbitatry subset of a Turing-recognizable language, is also a Turing-recognizable language?

A computably enumerable set $m$-reduces to the halting problem

Does there exist an Ordinal Turing Machine program which can detect the occurrence of accidentally writable reals on the tape of a simulated program?

Boolos’s proof of Gödel’s first incompleteness theorem. What am I getting wrong?

How will Mathematics courses help learning Computability Theory and Complexity Theory?

On Shoenfield's Mathematical Logic, Chapter 6 Q2

Sets which are strictly $\Sigma_n$ but not $\Sigma_n$-complete

Is this problem computable?

Showing that the diagonal set is $\Pi_k$

Bounded quantifiers don't count in arithmetic hierarchy

Proving equality of functions defined by primitive recursion

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