3
votes
1answer
125 views

Countable model theory for $\omega$-stable theories?

This is a bit of a fishing expedition, because I'm not sure what I'm looking for. Very vaguely stated, here's the driving question: What conditions on an $\omega$-stable theory make the class of ...
20
votes
6answers
4k views

What are some proofs of Godel's Theorem which are *essentially different* from the original proof?

I am looking for examples of proofs of Godel's (First) Incompleteness Theorem which are essentially different from (Rosser's improvement of) Godel's original proof. This is partly inspired by ...
8
votes
5answers
881 views

The use of the word “model” in Mathematical Logic vs the same word in Natural Sciences

I have always been wondering why the term "model" is used by mathematicians (especially in mathematical logic) in a conceptually different (even opposite) way than it is used by other scientists, ...
34
votes
5answers
2k views

Heuristic argument that finite simple groups _ought_ to be “classifiable”?

Obviously there exists a list of the finite simple groups, but why should it be a nice list, one that you can write down? Solomon's AMS article goes some way toward a historical / technical ...
5
votes
5answers
3k views

Models of ZFC Set Theory - Getting Started

For just any first-order theory: What are the sets I am supposed/allowed to think of when thinking of models as sets (of something + additional structure)? Provided: I can think of models of any ...
11
votes
4answers
2k views

Category theory and model theory as “natural” counterparts

I am aware of the profound discussion of the relationship between category theory and model theory (e.g. at The n-Category Café) but do wonder why category theory (CT) is not opposed to model theory ...