Question

formulas such that either "$\mathcal{M} \vDash \phi$, then $\mathcal{M} \vDash \psi$" or "$\mathcal{M} \vDash \phi \rightarrow \psi$"

score 134 · Answer 1 · 2026-03-26 21:53:59

134

Views

formulas such that either "$\mathcal{M} \vDash \phi$, then $\mathcal{M} \vDash \psi$" or "$\mathcal{M} \vDash \phi \rightarrow \psi$"

Published on 26 Mar 2026 - 21:53

score 196 · Answer 2 · 2026-03-25 03:03:47

196

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Why is $\forall x (x = x)$ an example of a first order sentence that is neither provable nor disprovable?

Published on 25 Mar 2026 - 3:03

score 236 · Answer 3 · 2026-03-26 08:02:18

236

Views

What is the intuitive explanation of $\exists y \theta(x,y) \to \psi(x)$ is the same to $\forall y ( \theta(x,y) \to \psi(x) )$?

Published on 26 Mar 2026 - 8:02

score 363 · Answer 4 · 2026-03-24 23:51:34

363

Views

Formal proof of $\exists x (\exists y P(y) \rightarrow P(x))$ and $(\forall x \exists y R(x,y))\rightarrow (\forall y \exists x R(y,x))$

Published on 24 Mar 2026 - 23:51

score 51 · Answer 5 · 2018-11-09 15:19:36

51

Views

Is $P→(Q∧R)$ the correct answer?

Published on 09 Nov 2018 - 15:19

score 261 · Answer 6 · 2026-03-25 17:45:15

261

Views

Associativity axiom expressed in first-order logic with predicates only

Published on 25 Mar 2026 - 17:45

score 72 · Answer 7 · 2018-11-10 08:28:33

72

Views

$\mathcal {N}\models \phi(n)$ if and only if $n$ is a power of 2, i.e. $n\in \{1,2,4,8,...\}$.

Published on 10 Nov 2018 - 8:28

score 59 · Answer 8 · 2026-03-25 20:11:57

59

Views

How does one formally show that bounded search with some property $R(a,x)$ is computable i.e. $\exists x \in \mathbf N (x < y \to R(a,x) )$?

Published on 25 Mar 2026 - 20:11

score 169 · Answer 9 · 2026-03-26 07:37:27

169

Views

Elementary substructure and existentially closed

Published on 26 Mar 2026 - 7:37

score 17 · Answer 10 · 2018-11-11 05:20:39

17

Views

Difference between two sentences

Published on 11 Nov 2018 - 5:20

score 104 · Answer 11 · 2026-03-26 11:17:31

104

Views

Proving that first-order formulas can not distinguish sets of a certain size

Published on 26 Mar 2026 - 11:17

score 28 · Answer 12 · 2018-11-12 18:30:12

Proof: is $ \forall x (P(x) \Leftrightarrow Q(x)) \Leftrightarrow (\forall x P(x) \Leftrightarrow \forall x Q(x))$

score 148 · Answer 13 · 2018-11-13 18:11:53

148

Views

How to make an English sentence from a first-order logic formula with unbound variables?

Published on 13 Nov 2018 - 18:11

score 56 · Answer 14 · 2018-11-13 23:21:14

56

Views

Expanding two iterated limits into quantifiers?

Published on 13 Nov 2018 - 23:21

score 568 · Answer 15 · 2026-03-26 22:13:20

568

Views

Is the reason that vacuous statements are True because empty L-structures are illegal?

Published on 26 Mar 2026 - 22:13

List Question

formulas such that either "$\mathcal{M} \vDash \phi$, then $\mathcal{M} \vDash \psi$" or "$\mathcal{M} \vDash \phi \rightarrow \psi$"

Why is $\forall x (x = x)$ an example of a first order sentence that is neither provable nor disprovable?

What is the intuitive explanation of $\exists y \theta(x,y) \to \psi(x)$ is the same to $\forall y ( \theta(x,y) \to \psi(x) )$?

Formal proof of $\exists x (\exists y P(y) \rightarrow P(x))$ and $(\forall x \exists y R(x,y))\rightarrow (\forall y \exists x R(y,x))$

Is $P→(Q∧R)$ the correct answer?

Associativity axiom expressed in first-order logic with predicates only

$\mathcal {N}\models \phi(n)$ if and only if $n$ is a power of 2, i.e. $n\in \{1,2,4,8,...\}$.

How does one formally show that bounded search with some property $R(a,x)$ is computable i.e. $\exists x \in \mathbf N (x < y \to R(a,x) )$?

Elementary substructure and existentially closed

Difference between two sentences

Proving that first-order formulas can not distinguish sets of a certain size

Proof: is $ \forall x (P(x) \Leftrightarrow Q(x)) \Leftrightarrow (\forall x P(x) \Leftrightarrow \forall x Q(x))$

How to make an English sentence from a first-order logic formula with unbound variables?

Expanding two iterated limits into quantifiers?

Is the reason that vacuous statements are True because empty L-structures are illegal?

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