Question

Prove Q is a theorem of T iff Q is a theorem of every consistent and complete extension of T

score 78 · Answer 1 · 2026-03-30 23:15:33

78

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Prove Q is a theorem of T iff Q is a theorem of every consistent and complete extension of T

Published on 30 Mar 2026 - 23:15

score 219 · Answer 2 · 2026-03-28 15:12:25

219

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Why is $\forall x\exists y(Fy \to Gx) \therefore \exists y\forall x(Fy \to Gx)$ valid, intuitively?

Published on 28 Mar 2026 - 15:12

score 70 · Answer 3 · 2026-03-29 22:34:38

70

Views

Characterizing $(\mathbb{Z}, <)$ up to isomorphism

Published on 29 Mar 2026 - 22:34

score 21 · Answer 4 · 2026-03-25 19:01:52

21

Views

Theory to Signature Mapping?

Published on 25 Mar 2026 - 19:01

score 48 · Answer 5 · 2020-04-05 06:03:52

48

Views

Is "$\forall X\in\Gamma\forall Y\in \Sigma\exists x(x\in X\wedge x\in Y)$" a well-formed second-order logic formula?

Published on 05 Apr 2020 - 6:03

score 131 · Answer 6 · 2020-04-05 16:04:34

131

Views

Temporal Logic of Actions: always and eventually definitions?

Published on 05 Apr 2020 - 16:04

score 124 · Answer 7 · 2026-03-28 02:23:44

124

Views

Characterization of V-stages in the absence of foundation or replacement

Published on 28 Mar 2026 - 2:23

score 97 · Answer 8 · 2026-03-30 23:15:35

97

Views

I am trying to show the relationship between logical consequence of Gamma and being true in every model of Gamma

Published on 30 Mar 2026 - 23:15

score 284 · Answer 9 · 2026-03-31 18:54:42

284

Views

Is infinitary first-order logic strictly more expressive than weak second-order logic?

Published on 31 Mar 2026 - 18:54

score 64 · Answer 10 · 2026-03-30 23:13:31

64

Views

Confusion on Proof of Marker Lemma 2.1.14, $T \vDash \phi \implies \exists \Delta \subseteq T, |\Delta| \in \mathbb{N} \land \Delta \vDash T$

Published on 30 Mar 2026 - 23:13

score 82 · Answer 11 · 2026-03-30 23:13:32

82

Views

Show that a wf $\mathscr{B}(t)⇒(\exists x_i)\mathscr{B}(x_i)$ logically valid if $t$ is free for $x_i$ in $\mathscr{B}$

Published on 30 Mar 2026 - 23:13

score 76 · Answer 12 · 2026-03-30 23:10:04

76

Views

Satisfiability and Truth in First Order Model Theory

Published on 30 Mar 2026 - 23:10

score 78 · Answer 13 · 2026-03-30 23:13:15

78

Views

Prove $(\forall x_i)(\mathscr{B}\rightarrow \mathscr{C})\rightarrow ((\forall x_i)\mathscr{B}⇒(\forall x_i)\mathscr{C})$ is logically valid

Published on 30 Mar 2026 - 23:13

score 66 · Answer 14 · 2020-04-09 17:20:03

66

Views

Contraposition over Universal and Existential Quantifiers

Published on 09 Apr 2020 - 17:20

score 108 · Answer 15 · 2026-03-26 09:16:29

108

Views

Proving $\forall x(x \text{ is odd} \to x^2 \text{ is odd)}$ using First Order Logic.

Published on 26 Mar 2026 - 9:16

List Question

Prove Q is a theorem of T iff Q is a theorem of every consistent and complete extension of T

Why is $\forall x\exists y(Fy \to Gx) \therefore \exists y\forall x(Fy \to Gx)$ valid, intuitively?

Characterizing $(\mathbb{Z}, <)$ up to isomorphism

Theory to Signature Mapping?

Is "$\forall X\in\Gamma\forall Y\in \Sigma\exists x(x\in X\wedge x\in Y)$" a well-formed second-order logic formula?

Temporal Logic of Actions: always and eventually definitions?

Characterization of V-stages in the absence of foundation or replacement

I am trying to show the relationship between logical consequence of Gamma and being true in every model of Gamma

Is infinitary first-order logic strictly more expressive than weak second-order logic?

Confusion on Proof of Marker Lemma 2.1.14, $T \vDash \phi \implies \exists \Delta \subseteq T, |\Delta| \in \mathbb{N} \land \Delta \vDash T$

Show that a wf $\mathscr{B}(t)⇒(\exists x_i)\mathscr{B}(x_i)$ logically valid if $t$ is free for $x_i$ in $\mathscr{B}$

Satisfiability and Truth in First Order Model Theory

Prove $(\forall x_i)(\mathscr{B}\rightarrow \mathscr{C})\rightarrow ((\forall x_i)\mathscr{B}⇒(\forall x_i)\mathscr{C})$ is logically valid

Contraposition over Universal and Existential Quantifiers

Proving $\forall x(x \text{ is odd} \to x^2 \text{ is odd)}$ using First Order Logic.

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