2
votes
1answer
41 views

Non-isomorpic uncountable dense linear orderings (a textbook example)

We know that two countable dense open orderings are isomorphic, and we know that this is generally not true for uncountable structures. Now I quote from the textbook, that is "Model-Theoretic Logics": ...
1
vote
1answer
86 views

Example of two finitely isomorphic structures (or $\omega$-isomorphic) that are not partially isomorphic?

One can define several maps between given structures in order to portray similarities or differences. The concept of isomorphism displays a deep structural overlapping, while for instance an ...
4
votes
1answer
67 views

Ultraproducts by countably complete ultrafilter

I've recently learned about ultraproducts, but the source I learned from almost immediately after the definitions restricted to talking about countably incomplete ultrafilters. I know that the ...
3
votes
1answer
156 views

Tarski-Vaught test for $\preceq$ reduction

The Tarski-Vaught test for $\preceq$ states that given a structure $\mathfrak{B}$ and $A\subseteq B$ then $A$ is the underlying set of an elementary substructure of $\mathfrak{B}$ iff for all formulas ...
4
votes
1answer
149 views

Are there simple counterexamples to a strengthening of omitting types theorem

The famous Ehrenfeucht's omitting types theorem states that for any countable set of nonisolated types (without parameters), there is a (countable) model such that it does not realize any of them. A ...
7
votes
2answers
128 views

What are the possible minimal acl-dimensions of strongly minimal models?

The question is as in title. By acl-dimension I understand the cardinality of maximal acl-independent set (well-defined for strongly minimal theories). By minimal I understand that there is no ...
3
votes
1answer
121 views

Automorphisms of elementary extensions

I think this is probably a very simple question, but I've been puzzling over it for a while and can't seem to get anywhere. Suppose $M$ is a structure, $\alpha$ is an automorphism of $M$, and $N$ is ...
2
votes
1answer
116 views

Give an example of a homogeneous, but not strongly homogeneous model

To avoid any confusion, the notions of (strong) homogeneity as I understand them are as follows: a model $M$ is said to be homogeneous if for any elementary partial function $f$ from the model into ...