Question

Show that PA has a denumerable model that is not isomorphic to N

score 129 · Answer 1 · 2021-04-19 02:11:49

129

Views

Show that PA has a denumerable model that is not isomorphic to N

Published on 19 Apr 2021 - 2:11

score 124 · Answer 2 · 2021-04-24 16:59:46

124

Views

deductive system where the axioms are all the propositions that are not tautology

Published on 24 Apr 2021 - 16:59

score 89 · Answer 3 · 2021-05-03 03:13:44

89

Views

Problem 17.2 from Computability and Logic By Boolos et all

Published on 03 May 2021 - 3:13

score 48 · Answer 4 · 2021-05-06 17:55:49

Understanding Textbook Proof: if theory $T$ is $\omega$-consistent, then if $\vdash_T \text{Prv}(\ulcorner A \urcorner)$ then $\vdash_T A$

score 102 · Answer 5 · 2021-05-09 02:54:25

102

Views

Computability and Logic by Boolos et all Problem 17.1

Published on 09 May 2021 - 2:54

score 59 · Answer 6 · 2021-05-10 21:15:48

59

Views

Godel's first Incompleteness Theorem: Truth vs Derivability/Consequence

Published on 10 May 2021 - 21:15

score 91 · Answer 7 · 2021-05-10 22:59:29

91

Views

Prove that the minimal finitely axiomatizable theory of arithmetic $\mathbf{Q}$ plus the Rosser sentence is consistent.

Published on 10 May 2021 - 22:59

score 45 · Answer 8 · 2021-05-11 01:37:18

45

Views

Show a model of $\mathbf{Q}$ where this is false $\forall x \forall y (x \cdot y = y \cdot x) $

Published on 11 May 2021 - 1:37

score 66 · Answer 9 · 2021-05-11 04:27:21

66

Views

Demonstrate a nondenumerable set of consistent extensions of $\mathbf{Q}$ that are pairwise inconsistent.

Published on 11 May 2021 - 4:27

score 135 · Answer 10 · 2021-06-14 22:34:07

135

Views

Finitary reasoning and the distinction between mathematical and metamathematical theorems

Published on 14 Jun 2021 - 22:34

score 317 · Answer 11 · 2021-06-24 19:05:32

317

Views

Can metalogic and model theory be formalized?

Published on 24 Jun 2021 - 19:05

score 173 · Answer 12 · 2026-03-23 21:52:08

173

Views

Why isn't math proofs just a computer trial and error?

Published on 23 Mar 2026 - 21:52

score 320 · Answer 13 · 2021-08-24 09:17:56

320

Views

Valid form and true premises makes an argument sound, but do 'premises' mean P, Q, R,... or 'what comprises the antecedent'?

Published on 24 Aug 2021 - 9:17

score 97 · Answer 14 · 2021-08-27 11:53:59

97

Views

Meta-Definition of Convergence

Published on 27 Aug 2021 - 11:53

score 328 · Answer 15 · 2021-08-30 10:38:32

328

Views

(Solution verification and criticism) If wff $\phi$ has no repetition of sentence letters, then $\nvDash \phi$

Published on 30 Aug 2021 - 10:38

List Question

Show that PA has a denumerable model that is not isomorphic to N

deductive system where the axioms are all the propositions that are not tautology

Problem 17.2 from Computability and Logic By Boolos et all

Understanding Textbook Proof: if theory $T$ is $\omega$-consistent, then if $\vdash_T \text{Prv}(\ulcorner A \urcorner)$ then $\vdash_T A$

Computability and Logic by Boolos et all Problem 17.1

Godel's first Incompleteness Theorem: Truth vs Derivability/Consequence

Prove that the minimal finitely axiomatizable theory of arithmetic $\mathbf{Q}$ plus the Rosser sentence is consistent.

Show a model of $\mathbf{Q}$ where this is false $\forall x \forall y (x \cdot y = y \cdot x) $

Demonstrate a nondenumerable set of consistent extensions of $\mathbf{Q}$ that are pairwise inconsistent.

Finitary reasoning and the distinction between mathematical and metamathematical theorems

Can metalogic and model theory be formalized?

Why isn't math proofs just a computer trial and error?

Valid form and true premises makes an argument sound, but do 'premises' mean P, Q, R,... or 'what comprises the antecedent'?

Meta-Definition of Convergence

(Solution verification and criticism) If wff $\phi$ has no repetition of sentence letters, then $\nvDash \phi$

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