Question

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

score 88 · Answer 1 · 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 61 · Answer 2 · 2026-03-29 15:54:49

61

Views

Show that $\{\alpha<\omega_1 : L_\alpha \prec L_{\omega_1}\}$ is closed unbounded in $\omega_1$.

Published on 29 Mar 2026 - 15:54

score 36 · Answer 3 · 2023-11-17 04:56:03

36

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 17 Nov 2023 - 4:56

score 368 · Answer 4 · 2023-11-17 05:23:13

368

Views

Counter example to Ryll-Nardzewski

Published on 17 Nov 2023 - 5:23

score 40 · Answer 5 · 2023-11-18 16:36:08

40

Views

Examples where homogeneity is better proved via atomicity

Published on 18 Nov 2023 - 16:36

score 63 · Answer 6 · 2023-11-19 12:45:49

63

Views

A recursive axiomatization of the theory of real addition and real multiplication

Published on 19 Nov 2023 - 12:45

score 131 · Answer 7 · 2023-11-19 14:21:30

131

Views

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

Published on 19 Nov 2023 - 14:21

score 299 · Answer 8 · 2023-11-20 19:01:29

299

Views

Book recommendation for Model Theory

Published on 20 Nov 2023 - 19:01

score 47 · Answer 9 · 2023-11-23 16:30:55

47

Views

In the transitive closure of $\in$, is the empty set the least element?

Published on 23 Nov 2023 - 16:30

score 104 · Answer 10 · 2023-11-24 18:31:31

104

Views

Definition of witness property in Marker's "Model theory - An introduction"

Published on 24 Nov 2023 - 18:31

score 58 · Answer 11 · 2023-11-25 00:17:21

58

Views

Formal definition of the union of two structures over the same set

Published on 25 Nov 2023 - 0:17

score 61 · Answer 12 · 2023-11-26 14:19:56

61

Views

Why is the cardinality of a first-order language max{$\aleph_0, k$}?

Published on 26 Nov 2023 - 14:19

score 99 · Answer 13 · 2023-11-26 22:43:03

99

Views

Count the number of non-isomorphic models for a theory $T$ describing infinitely branching equivalence classes, each class infinite

Published on 26 Nov 2023 - 22:43

score 125 · Answer 14 · 2026-03-25 03:01:19

125

Views

Prove that divisibility between two natural numbers is not definable in arithmetic

Published on 25 Mar 2026 - 3:01

score 64 · Answer 15 · 2023-11-27 14:44:32

$tp^\mathbb{Q}(a/\mathbb N) = tp^\mathbb{Q}(b/\mathbb N)$ iff there is an automorphism $\sigma$ of $\mathbb Q$ fixing $\mathbb N$ and $\sigma(a)=b$

List Question

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

Show that $\{\alpha<\omega_1 : L_\alpha \prec L_{\omega_1}\}$ is closed unbounded in $\omega_1$.

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

Counter example to Ryll-Nardzewski

Examples where homogeneity is better proved via atomicity

A recursive axiomatization of the theory of real addition and real multiplication

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

Book recommendation for Model Theory

In the transitive closure of $\in$, is the empty set the least element?

Definition of witness property in Marker's "Model theory - An introduction"

Formal definition of the union of two structures over the same set

Why is the cardinality of a first-order language max{$\aleph_0, k$}?

Count the number of non-isomorphic models for a theory $T$ describing infinitely branching equivalence classes, each class infinite

Prove that divisibility between two natural numbers is not definable in arithmetic

$tp^\mathbb{Q}(a/\mathbb N) = tp^\mathbb{Q}(b/\mathbb N)$ iff there is an automorphism $\sigma$ of $\mathbb Q$ fixing $\mathbb N$ and $\sigma(a)=b$

Trending Questions

Popular # Hahtags

Popular Questions