Any recommendations on the best texts for introducing Model Theory?
closed as too broad by Willie Wong, coudy, Alex Degtyarev, Stefan Kohl, Johannes Hahn Apr 29 '15 at 12:25
There are either too many possible answers, or good answers would be too long for this format. Please add details to narrow the answer set or to isolate an issue that can be answered in a few paragraphs.If this question can be reworded to fit the rules in the help center, please edit the question.
I would suggest Hodges larger book (Model theory, vol. 42 in the Encyclopedia of Mathematics and its applications).
One of the reasons is that he does not center only on first-order structures, so you get a good idea of the richness and possibilities of the field. (For classical model theory of first-order structures, Chang and Keisler is the encyclopedic work, and you may want to look into it after, if you want to complement what Hodges covers.)
Another reason is the many applications (in mainstream mathematics, not just within logic) that the book presents, both in the text and the exercises. (There are some beautiful "typical" applications one sees frequently, such as the Ax-Kochen theorem, or the development of the theory of real closed fields. Hodges really covers many more, and one sees these examples as forming patterns and revealing possibilities. Modern applications within number theory and algebraic geometry show how useful and fruitful pursuing this is. In this respect, after this book, you may want to look at Model Theory, Algebra, and Geometry, Haskell, Pillay, and Steinhorn, eds., MSRI publications.)
Finally, its treatment of stability theory, which is central to modern research in the field, is excellent. In this respect, Chang and Keisler feels sadly a bit dated. (After, you may want to continue with An introduction to stability theory by Pillay, and if you want to go further, with Pillay's other book, Geometric stability theory.)