Question

How can $(\exists x\in Z)(\forall y\in Z)(x>y)$ and its negation, $(\forall x\in Z)(\exists y\in Z)(x\le y)$, both be true?

score 1.4k · Answer 1 · 2026-03-28 01:26:16

1.4k

Views

How can $(\exists x\in Z)(\forall y\in Z)(x>y)$ and its negation, $(\forall x\in Z)(\exists y\in Z)(x\le y)$, both be true?

Published on 28 Mar 2026 - 1:26

score 1.1k · Answer 2 · 2026-03-28 01:25:49

1.1k

Views

In this problem, A(x) and B(x) are two predicates over the same domain.

Published on 28 Mar 2026 - 1:25

score 69 · Answer 3 · 2026-03-30 08:24:10

69

Views

Show that $ \forall x (f g x = x) \not \models \forall x (g f x = x) $

Published on 30 Mar 2026 - 8:24

score 49 · Answer 4 · 2026-03-28 01:26:07

49

Views

Is this proof involving quantifiers valid?

Published on 28 Mar 2026 - 1:26

score 343 · Answer 5 · 2019-10-10 00:26:45

343

Views

definition of a number approach to $\infty$ in first-order-logic

Published on 10 Oct 2019 - 0:26

score 1.2k · Answer 6 · 2026-03-30 08:29:52

1.2k

Views

Best book for first order predicate logic

Published on 30 Mar 2026 - 8:29

score 56 · Answer 7 · 2026-02-24 07:07:39

56

Views

How much actual computer mathematics programs can be done in this extremely weak concrete set theory?

Published on 24 Feb 2026 - 7:07

score 104 · Answer 8 · 2026-03-25 22:03:44

104

Views

About inconsistency of first order set theories?

Published on 25 Mar 2026 - 22:03

score 201 · Answer 9 · 2026-03-29 03:27:37

201

Views

Length and Complexity of a Proof

Published on 29 Mar 2026 - 3:27

score 335 · Answer 10 · 2026-03-28 01:25:54

335

Views

How to find a counter-model for a formula with implication and only one variable.

Published on 28 Mar 2026 - 1:25

score 82 · Answer 11 · 2019-10-11 23:37:21

Given a $\mathcal{L}=\{0,1,+,\cdot , R\}$ and structure $C=(\mathbb{C},...)$ give a formula so that $C\models \phi(x)$ iff $x$ is a real number

score 166 · Answer 12 · 2019-10-12 08:43:42

166

Views

FOL: Is it possible for a ≠ a for some term a?

Published on 12 Oct 2019 - 8:43

score 201 · Answer 13 · 2026-03-25 06:09:27

201

Views

FOL - Countermodel for argument without predicates

Published on 25 Mar 2026 - 6:09

score 101 · Answer 14 · 2019-10-14 12:59:04

101

Views

What is the consistency strength of negating Banach-Tarski paradox?

Published on 14 Oct 2019 - 12:59

score 349 · Answer 15 · 2019-10-14 21:14:56

349

Views

Proof: If x occurs free in either φ or ψ, then x occurs free in (φ◦ψ) for ◦ = ∧,∨,→,↔

Published on 14 Oct 2019 - 21:14

List Question

How can $(\exists x\in Z)(\forall y\in Z)(x>y)$ and its negation, $(\forall x\in Z)(\exists y\in Z)(x\le y)$, both be true?

In this problem, A(x) and B(x) are two predicates over the same domain.

Show that $ \forall x (f g x = x) \not \models \forall x (g f x = x) $

Is this proof involving quantifiers valid?

definition of a number approach to $\infty$ in first-order-logic

Best book for first order predicate logic

How much actual computer mathematics programs can be done in this extremely weak concrete set theory?

About inconsistency of first order set theories?

Length and Complexity of a Proof

How to find a counter-model for a formula with implication and only one variable.

Given a $\mathcal{L}=\{0,1,+,\cdot , R\}$ and structure $C=(\mathbb{C},...)$ give a formula so that $C\models \phi(x)$ iff $x$ is a real number

FOL: Is it possible for a ≠ a for some term a?

FOL - Countermodel for argument without predicates

What is the consistency strength of negating Banach-Tarski paradox?

Proof: If x occurs free in either φ or ψ, then x occurs free in (φ◦ψ) for ◦ = ∧,∨,→,↔

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