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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.

Belgi
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user167137
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    It's hard to be an algebra book aimed at model theory without being a model theory book. That said, Marker's Model Theory deals more thoroughly with connections to algebra than Hodges does, though this comes hand in hand with more serious algebraic prerequisites at times. – Alex Kruckman Jul 30 '14 at 21:34
  • It might be easier to answer if you were more specific about what sorts of things from Hodges you're having trouble with. – Alex Kruckman Jul 30 '14 at 21:35
  • Keisler and Chang, if you want an algebraic approach. – user40276 Jul 31 '14 at 02:05
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    @user40276 Really? I've always thought of Chang and Keisler as the least algebraically oriented of the major model theory texts. You'll find a lot more set theory than field theory in C&K! – Alex Kruckman Jul 31 '14 at 06:08
  • @AlexKruckman: C&K actually has a chapter dedicated to the application of model theory to field theory. That being said, I still agree with you that it is the least algebraic of the bunch. – Kyle Gannon Aug 05 '14 at 23:07

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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).

Kyle Gannon
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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.

Nagase
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