User Primo Petri

10 votes

Is there a nonstandard model of Peano's arithmetic where any element has only finitely many prime divisors?

answered Feb 17, 2022 at 11:18

7 votes

Accepted

Sentence equivalent to $\bigwedge_{i=1}^ \infty \sigma_i$ without using infinite conjunctions

answered Mar 5, 2022 at 17:52

7 votes

Examples of classes of structures which are "surprisingly" axiomatizable.

answered Jan 6 at 15:41

6 votes

Better understanding dividing and forking

answered Apr 28, 2022 at 22:33

6 votes

Accepted

You don't need to take an algebraic closure twice in model theory

answered Sep 20, 2014 at 7:46

5 votes

Is the (first order theory) of Hilbert spaces categorical?

answered Oct 1, 2014 at 14:26

5 votes

In what sense of "structure" do group homomorphisms "preserve structure"?

answered Feb 21, 2015 at 7:18

5 votes

Accepted

substructures, superstructures, and their elementary counterparts

answered Feb 27, 2015 at 17:43

5 votes

Accepted

Complete $n$-types for the theories of $( \mathbb Z , s )$ and $( \mathbb Z , s , < )$

answered Apr 15, 2015 at 4:21

5 votes

Why are structures with no relations called algebras?

answered Apr 22, 2015 at 5:26

5 votes

How to express a function $f:A\rightarrow B$ as a first order structure?

answered Jun 19, 2022 at 7:14

5 votes

Accepted

Exercise about ultraproducts

answered Jan 17, 2022 at 15:00

5 votes

Accepted

How to Learn Stability Theory

answered Sep 16, 2017 at 13:59

5 votes

Is algebra needed to really understand and/or enjoy model theory?

answered May 18, 2015 at 18:08

5 votes

Accepted

Weakly Saturated model not Saturated

answered May 5 at 12:31

4 votes

Compactness theorem for monster models

answered Jul 5, 2022 at 12:12

4 votes

What is the modern convention for these model theory defintions?

answered Jun 1, 2022 at 18:09

4 votes

Accepted

Classifying complete extensions of a theory with countable atomic (prime) models

answered Mar 17, 2022 at 21:31

4 votes

Accepted

Order preserving map from interval $(0,1)$ to the ultrafilter

answered Mar 15, 2022 at 20:47

4 votes

Accepted

Is definable $\emptyset$-definable?

answered Feb 19, 2015 at 9:15

4 votes

Accepted

Are ideals necessarily definable?

answered Sep 13, 2014 at 9:27

4 votes

No countable models

answered Mar 28, 2015 at 14:02

3 votes

Prove that for an arbitrary (possibly infinite) language, that for a finite L-structure $M$, if $M \equiv N$ then $ M \cong N$

answered Jan 13, 2015 at 6:48

3 votes

Accepted

Are there elementarily equivalent models $\mathcal{M}, \mathcal{N}$ of the same cardinality s.t. neither can be elementarily embedded into the other?

answered Jan 19, 2015 at 5:57

3 votes

Accepted

Sequence of indiscernibles in a theory with an equivalence relation with infinitely many equivalence classes

answered May 1, 2015 at 4:39

3 votes

Every theory eliminates quantifiers in an appropriate definitional expansion?

answered May 9, 2015 at 7:58

3 votes

Accepted

Functions or relations stable under automorphism

answered May 25, 2015 at 15:39

3 votes

Orbit of an element $a$ over a set $A$ in the monster model.

answered Jun 3, 2015 at 9:58

3 votes

Prove completeness from elimination of quantifiers

answered Feb 6, 2022 at 13:47

3 votes

Disjoint union of copies of Henson graph is not homogenous

answered Mar 16, 2022 at 12:49

Stack Exchange Network

78 Answers

Is there a nonstandard model of Peano's arithmetic where any element has only finitely many prime divisors?

Sentence equivalent to $\bigwedge_{i=1}^ \infty \sigma_i$ without using infinite conjunctions

Examples of classes of structures which are "surprisingly" axiomatizable.

Better understanding dividing and forking

You don't need to take an algebraic closure twice in model theory

Is the (first order theory) of Hilbert spaces categorical?

In what sense of "structure" do group homomorphisms "preserve structure"?

substructures, superstructures, and their elementary counterparts

Complete $n$-types for the theories of $( \mathbb Z , s )$ and $( \mathbb Z , s , < )$

Why are structures with no relations called algebras?

How to express a function $f:A\rightarrow B$ as a first order structure?

Exercise about ultraproducts

How to Learn Stability Theory

Is algebra needed to really understand and/or enjoy model theory?

Weakly Saturated model not Saturated

Compactness theorem for monster models

What is the modern convention for these model theory defintions?

Classifying complete extensions of a theory with countable atomic (prime) models

Order preserving map from interval $(0,1)$ to the ultrafilter

Is definable $\emptyset$-definable?

Are ideals necessarily definable?

No countable models

Prove that for an arbitrary (possibly infinite) language, that for a finite L-structure $M$, if $M \equiv N$ then $ M \cong N$

Are there elementarily equivalent models $\mathcal{M}, \mathcal{N}$ of the same cardinality s.t. neither can be elementarily embedded into the other?

Sequence of indiscernibles in a theory with an equivalence relation with infinitely many equivalence classes

Every theory eliminates quantifiers in an appropriate definitional expansion?

Functions or relations stable under automorphism

Orbit of an element $a$ over a set $A$ in the monster model.

Prove completeness from elimination of quantifiers

Disjoint union of copies of Henson graph is not homogenous