Question

Is $x$ a free variable in sentences like "$x\lt 7\Rightarrow x\lt 5$"?

score 85 · Answer 1 · 2023-11-09 05:30:18

Is $x$ a free variable in sentences like "$x\lt 7\Rightarrow x\lt 5$"?

Published on 09 Nov 2023 - 5:30

score 79 · Answer 2 · 2026-04-03 18:56:33

$\varphi$ is quantifier free sentence, $T$ a theory, $\vec{c} \not\in T$. $T \vdash \varphi(\vec{c})$ implies $T \vdash \forall x \varphi(\vec{x})$?

score 59 · Answer 3 · 2026-04-10 23:13:01

59

Views

Any formula is logically equivalent to a formula with all terms of height ≤ 1.

Published on 10 Apr 2026 - 23:13

score 54 · Answer 4 · 2026-04-09 21:30:10

54

Views

A question about 2.26 in Mendelson's Introduction to Logic

Published on 09 Apr 2026 - 21:30

score 27 · Answer 5 · 2026-04-10 09:31:24

27

Views

Herbrand Structure

Published on 10 Apr 2026 - 9:31

score 53 · Answer 6 · 2026-04-03 00:01:33

53

Views

proof of that we can find a sentence σ s.t. σ is true in theory A but not deducible from A

Published on 03 Apr 2026 - 0:01

score 48 · Answer 7 · 2026-04-03 00:00:58

48

Views

proving that $\mathcal{M}\models\forall x\phi\wedge\psi\implies\mathcal{M}\models\forall x(\phi\wedge\psi)$

Published on 03 Apr 2026 - 0:00

score 36 · Answer 8 · 2026-04-11 02:57:00

First order logic - finding an L-sentence satisfiable in some structure with an infinite domain but is false in every structure with a finite domain.

score 53 · Answer 9 · 2026-04-03 00:00:05

53

Views

Prove that there is a sentence $\phi$ such that $\cal N\models \phi$ iff $\cal N \cong \cal M$ if $\cal L$ and $\cal M$ are finite

Published on 03 Apr 2026 - 0:00

score 88 · Answer 10 · 2026-04-02 07:55:56

88

Views

When we say "cardinality of first order language L" and "cardinality of a structure or model" what we are meaning?

Published on 02 Apr 2026 - 7:55

score 838 · Answer 11 · 2026-04-11 04:54:07

838

Views

Nonstandard infinite / hyperfinite sum in IST

Published on 11 Apr 2026 - 4:54

score 107 · Answer 12 · 2026-04-10 18:02:01

107

Views

Is ZFC independent of the logic used?

Published on 10 Apr 2026 - 18:02

score 37 · Answer 13 · 2026-04-03 01:37:59

37

Views

Let $DLO$ be the theory of dense linear orders, $c_i$ be new constant symbols, and $DLO'=DLO \cup \{ c_i < c_{i+1} \}$. Then $DLO'$ is complete

Published on 03 Apr 2026 - 1:37

score 132 · Answer 14 · 2026-04-03 01:39:51

132

Views

Prove that the set of nonprime numbers $>0$ is a spectrum

Published on 03 Apr 2026 - 1:39

score 107 · Answer 15 · 2026-03-25 09:25:22

107

Views

Proof of contraposition theorem using logical (semantic) entailment definition

Published on 25 Mar 2026 - 9:25

List Question

Is $x$ a free variable in sentences like "$x\lt 7\Rightarrow x\lt 5$"?

$\varphi$ is quantifier free sentence, $T$ a theory, $\vec{c} \not\in T$. $T \vdash \varphi(\vec{c})$ implies $T \vdash \forall x \varphi(\vec{x})$?

Any formula is logically equivalent to a formula with all terms of height ≤ 1.

A question about 2.26 in Mendelson's Introduction to Logic

Herbrand Structure

proof of that we can find a sentence σ s.t. σ is true in theory A but not deducible from A

proving that $\mathcal{M}\models\forall x\phi\wedge\psi\implies\mathcal{M}\models\forall x(\phi\wedge\psi)$

First order logic - finding an L-sentence satisfiable in some structure with an infinite domain but is false in every structure with a finite domain.

Prove that there is a sentence $\phi$ such that $\cal N\models \phi$ iff $\cal N \cong \cal M$ if $\cal L$ and $\cal M$ are finite

When we say "cardinality of first order language L" and "cardinality of a structure or model" what we are meaning?

Nonstandard infinite / hyperfinite sum in IST

Is ZFC independent of the logic used?

Let $DLO$ be the theory of dense linear orders, $c_i$ be new constant symbols, and $DLO'=DLO \cup \{ c_i < c_{i+1} \}$. Then $DLO'$ is complete

Prove that the set of nonprime numbers $>0$ is a spectrum

Proof of contraposition theorem using logical (semantic) entailment definition

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