[Math] Model Theory and Topology Connections

Question

I have studied a bit of model theory, when I say "a bit" I have studied much more than is available to a typical undergraduate in the UK (i think, certainly from what I have seen) but I am sure this is all introductory material when looked at on a bigger scale (as things always are) but it is the area that I am going to pursue in my masters degree next year and hopefully beyond.

I have also done some very introductory material in topology, sort of covered a typical "intro to topology" book.

What I was wanting to ask about was the connections between the two. Now I know that there are many strong connections, but I am yet to actually come across any of these connections (apart from reading things which says they exists and hearing people talk about these connections very generally).

So I was wondering if anyone could give me some idea as to where the connections lie and some references for reading about this. I am aware that there is something called "o-minimality" but I have no idea what this is, so I was looking for some good references. Also as I stated above I have an introductory grasp on topology so is it the case that I need to learn much more before I can grasp these connections at all?

(I would also like to add that I am not really sure what I am asking about, as I'm sure is obvious from the question, so please feel free to tell me that I'm looking for the wrong things or my questions is too naive.)

As always any help is greatly appreciated.

Answer 1

You can start by reading Alan Dow's paper:

Dow, A. An introduction to applications of elementary submodels to topology. Topology Proc. 13 (1988), no. 1, 17–72. MR1031969