Learning Model Theory

Question

What books/notes should one read to learn model theory? As I do not have much background in logic it would be ideal if such a reference does not assume much background in logic. Also, as I am interested in arithmetic geometry, is there a reference with a view towards such a topic?

Answer 1

I really like Introduction to Model Theory by David Marker. It starts from scratch and has a lot of algebraic examples.

Answer 2

You could give Bruno Poizat's A Course in Model Theory a try.

If you are feeling particularly ambitious, perhaps Model Theory and Algebraic Geometry (E. Bouscaren, ed.), which intends to gives an introduction to certain concepts in the interplay of model theory and algebraic geometry, with a view to an exposition of Hrushovski's proof of the geometric Mordell-Lang Conjecture. If nothing else, this work should give an idea of what concepts of model theory have found application in algebraic geometry (at least in the aforementioned proof), which should give you an idea of perhaps what topics to look for in a model theory text.

Answer 3

Also, as I am interested in arithmetic geometry, is there a reference with a view towards such a topic?

One paper I was able to find was Model Theory and Diophantine Geometry by Anand Pillay

Answer 4

For a free alternative, Peter L. Clark has posted his notes Introduction to Model Theory on his website. He says no prior knowledge of logic is assumed and the applications are primarily in the areas of Algebra, Algebraic Geometry and Number Theory.

Answer 5

There are a bunch of suggestions on Peter Smith's blog.

Answer 6

Besides Marker, for basic model theory I also recommend Barwise's compilation "Handbook of mathematical logic", Chang, Keisler & Troelstra's "Model theory" and Wilfrid Hodges' "Model theory" (he's also written "A shorter model theory", but I haven't seen it.).

However, I've only ever used them as reference, not as an actual textbook, so I can't guarantee their quality as such.

Answer 7

I found these notes by Stephen Simpson very useful.

Answer 8

These notes by Stefan Geschke have been extremely helpful to me. I currently taking the course these notes are based on and often I find the exposition (and the proofs) here much more illuminating than Marker's text. The goal of these notes is to prove Morley's Categoricity Theorem. If one is already using a tradional text, such as Marker, these notes are at least a very good companion to Marker.