Question

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

score 132 · Answer 1 · 2026-04-12 15:21:35

132

Views

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

Published on 12 Apr 2026 - 15:21

score 127 · Answer 2 · 2026-04-14 11:29:43

127

Views

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

Published on 14 Apr 2026 - 11:29

score 92 · Answer 3 · 2026-04-13 06:02:10

92

Views

Problem 17.2 from Computability and Logic By Boolos et all

Published on 13 Apr 2026 - 6:02

score 51 · Answer 4 · 2026-04-16 03:43:22

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

score 105 · Answer 5 · 2026-04-11 23:34:44

105

Views

Computability and Logic by Boolos et all Problem 17.1

Published on 11 Apr 2026 - 23:34

score 64 · Answer 6 · 2026-04-17 14:52:36

64

Views

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

Published on 17 Apr 2026 - 14:52

score 93 · Answer 7 · 2026-04-17 12:19:38

93

Views

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

Published on 17 Apr 2026 - 12:19

score 48 · Answer 8 · 2026-04-17 12:25:46

48

Views

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

Published on 17 Apr 2026 - 12:25

score 69 · Answer 9 · 2026-04-15 07:55:15

69

Views

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

Published on 15 Apr 2026 - 7:55

score 138 · Answer 10 · 2026-04-12 08:55:06

138

Views

Finitary reasoning and the distinction between mathematical and metamathematical theorems

Published on 12 Apr 2026 - 8:55

score 320 · Answer 11 · 2026-04-11 22:42:00

320

Views

Can metalogic and model theory be formalized?

Published on 11 Apr 2026 - 22:42

score 174 · Answer 12 · 2026-04-09 08:05:28

174

Views

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

Published on 09 Apr 2026 - 8:05

score 323 · Answer 13 · 2026-04-16 07:41:53

323

Views

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

Published on 16 Apr 2026 - 7:41

score 101 · Answer 14 · 2026-05-10 14:36:57

101

Views

Meta-Definition of Convergence

Published on 10 May 2026 - 14:36

score 331 · Answer 15 · 2026-04-13 19:48:22

331

Views

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

Published on 13 Apr 2026 - 19:48

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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