Question

Prove that if $\mathcal L$ is the empty language and $C$ is the set of structures $\mathcal M_n := \{1,...,n\}$ then $\text{Th}_a(C)$ is complete

score 91 · Answer 1 · 2023-10-26 05:50:01

91

Views

Prove that if $\mathcal L$ is the empty language and $C$ is the set of structures $\mathcal M_n := \{1,...,n\}$ then $\text{Th}_a(C)$ is complete

Published on 26 Oct 2023 - 5:50

score 53 · Answer 2 · 2023-10-27 01:16:23

53

Views

Tuple of structure and its element

Published on 27 Oct 2023 - 1:16

score 81 · Answer 3 · 2026-04-02 05:23:36

81

Views

How do we reconcile Solovay’s Model with the Hanh Banach Theorem in ZF

Published on 02 Apr 2026 - 5:23

score 101 · Answer 4 · 2026-03-27 12:14:27

101

Views

On the consistency of satisfiable first order theories

Published on 27 Mar 2026 - 12:14

score 57 · Answer 5 · 2023-11-02 21:05:55

57

Views

If a model of T has an elementary extension to a model of T', then all models of T have such an elementary extension

Published on 02 Nov 2023 - 21:05

score 166 · Answer 6 · 2023-11-05 13:22:23

166

Views

O-minimality and Putnam Competition

Published on 05 Nov 2023 - 13:22

score 102 · Answer 7 · 2023-11-06 16:15:22

102

Views

Multi-sorted model theory

Published on 06 Nov 2023 - 16:15

score 62 · Answer 8 · 2023-11-08 14:04:35

62

Views

Why does the reverse of Existential Generalisation not hold?

Published on 08 Nov 2023 - 14:04

score 131 · Answer 9 · 2023-11-08 16:55:32

131

Views

If A is a substructure of B and A is isomorphic to B then A is an elementary substructure of B

Published on 08 Nov 2023 - 16:55

score 65 · Answer 10 · 2026-03-25 12:49:44

65

Views

Connection of axioms of first order logic and axioms of first order theory

Published on 25 Mar 2026 - 12:49

score 103 · Answer 11 · 2023-11-09 13:36:15

103

Views

Abelian definable groups.

Published on 09 Nov 2023 - 13:36

score 52 · Answer 12 · 2023-11-11 17:08:25

52

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 11 Nov 2023 - 17:08

score 47 · Answer 13 · 2023-11-12 01:07:09

47

Views

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

Published on 12 Nov 2023 - 1:07

score 79 · Answer 14 · 2026-03-29 19:52:45

79

Views

Given an axiomatics, can you use its model to prove a theorem in that axiomatic?

Published on 29 Mar 2026 - 19:52

score 52 · Answer 15 · 2023-11-12 23:42:39

52

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 12 Nov 2023 - 23:42

List Question

Prove that if $\mathcal L$ is the empty language and $C$ is the set of structures $\mathcal M_n := \{1,...,n\}$ then $\text{Th}_a(C)$ is complete

Tuple of structure and its element

How do we reconcile Solovay’s Model with the Hanh Banach Theorem in ZF

On the consistency of satisfiable first order theories

If a model of T has an elementary extension to a model of T', then all models of T have such an elementary extension

O-minimality and Putnam Competition

Multi-sorted model theory

Why does the reverse of Existential Generalisation not hold?

If A is a substructure of B and A is isomorphic to B then A is an elementary substructure of B

Connection of axioms of first order logic and axioms of first order theory

Abelian definable groups.

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

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

Given an axiomatics, can you use its model to prove a theorem in that axiomatic?

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

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