Question

Is it possible to write a program that takes a natural number n as input, and finds the shortest arithmetic formula which computes n?

score 109 · Answer 1 · 2020-10-27 07:36:37

Is it possible to write a program that takes a natural number n as input, and finds the shortest arithmetic formula which computes n?

score 93 · Answer 2 · 2026-02-23 21:13:17

93

Views

Show that $G_{u,v}$ is not decidable and not recognizable (nor is its complement)

Published on 23 Feb 2026 - 21:13

score 123 · Answer 3 · 2026-04-03 03:30:09

123

Views

Locating the set in the arithmetic hierarchy

Published on 03 Apr 2026 - 3:30

score 373 · Answer 4 · 2020-10-28 00:34:12

373

Views

Computability -- prove the program does or does not exist

Published on 28 Oct 2020 - 0:34

score 1.1k · Answer 5 · 2026-03-27 23:12:49

1.1k

Views

Constructive vs computable real numbers

Published on 27 Mar 2026 - 23:12

score 72 · Answer 6 · 2026-03-29 14:54:35

72

Views

Recognizable not decidable subset

Published on 29 Mar 2026 - 14:54

score 104 · Answer 7 · 2026-02-23 21:17:31

104

Views

Boolos’s proof of the first incompleteness theorem. Predicate $C(x,y)$ and assumption of completeness.

Published on 23 Feb 2026 - 21:17

score 17 · Answer 8 · 2026-04-03 03:28:30

17

Views

If $R$ is $\Sigma_n$ and $(x,y)\in A\iff (\forall z < y) R(x,y,z)$, then $A$ is $\Sigma_n$

Published on 03 Apr 2026 - 3:28

score 35 · Answer 9 · 2026-04-03 03:26:10

35

Views

Confusion about writing $Inf$ as a $\Pi_2$ set

Published on 03 Apr 2026 - 3:26

score 96 · Answer 10 · 2020-11-10 08:50:04

96

Views

Identities involving addition, subtraction and absolute value

Published on 10 Nov 2020 - 8:50

score 1.7k · Answer 11 · 2026-03-29 14:55:32

1.7k

Views

How to prove a function is computable?

Published on 29 Mar 2026 - 14:55

score 157 · Answer 12 · 2026-03-28 21:26:06

157

Views

Incompleteness Theorems for Limit-Computable Formal Systems

Published on 28 Mar 2026 - 21:26

score 100 · Answer 13 · 2026-03-26 16:05:12

100

Views

A question about undecidable sentences with purely mathematical contents

Published on 26 Mar 2026 - 16:05

score 399 · Answer 14 · 2026-04-05 16:09:20

399

Views

Extensions of the Turing jump

Published on 05 Apr 2026 - 16:09

score 713 · Answer 15 · 2026-02-23 13:35:36

713

Views

How to prove undecidability other than Rice Theorem?

Published on 23 Feb 2026 - 13:35

List Question

Is it possible to write a program that takes a natural number n as input, and finds the shortest arithmetic formula which computes n?

Show that $G_{u,v}$ is not decidable and not recognizable (nor is its complement)

Locating the set in the arithmetic hierarchy

Computability -- prove the program does or does not exist

Constructive vs computable real numbers

Recognizable not decidable subset

Boolos’s proof of the first incompleteness theorem. Predicate $C(x,y)$ and assumption of completeness.

If $R$ is $\Sigma_n$ and $(x,y)\in A\iff (\forall z < y) R(x,y,z)$, then $A$ is $\Sigma_n$

Confusion about writing $Inf$ as a $\Pi_2$ set

Identities involving addition, subtraction and absolute value

How to prove a function is computable?

Incompleteness Theorems for Limit-Computable Formal Systems

A question about undecidable sentences with purely mathematical contents

Extensions of the Turing jump

How to prove undecidability other than Rice Theorem?

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