Best algebra text for Model Theory

Question

I'm looking for an algebra book that is tailored towards some of the ideas in Model Theory, I'm currently slogging through Hodges' Model Theory. I'm a bit rusty with my algebra and was curious if there are algebra texts aimed at Model Theory.

Answer 1

If you want a (model theory) text which gives a lot of examples (including a ton of algebraic examples) I suggest looking into Markers book, Model Theory: An Introduction. Warning : The book does have some errors and so you need to make sure you understand the material so that you don't get confused.

For an algebra text which eventually combines algebra with model theory, I would recommend looking at A Course in Universal Algebra by Stanley Burris and H.P. Sankappanavar. The book is about universal algebra, but the last chapter ties it together nicely with model theory.

Finally, there is a really nice section in Chang and Keisler which deals with the application of model theory to field theory (I believe it is in chapter 5). Other than that, this source is geared toward Ultraproducts and Ultrapowers as well as more abstract model theory (However, it is not as abstract as say, Shelah's Classification Theory).

Answer 2

I know this is a bit old, but two other references that may be worth looking into are Grätzer's Universal Algebra and Mal'cev's Algebraic Systems. They both contain material on model theory and are done "in the spirit", so to speak, of this discipline. I specially Mal'cev's book; although its notation is a bit non-standard, I found the explanations relatively clear and it helped me a lot with understanding some of the tougher parts of model theory.