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Any recommendations on the best texts for introducing Model Theory?

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  • $\begingroup$ To whom? Over what period of time? With what prerequisites? $\endgroup$
    – Andrés E. Caicedo
    Commented Jul 28, 2013 at 2:34
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    $\begingroup$ I would recommend Hodges A Shorter Model Theory to start. There's also Chang and Keisler's classic Model Theory. Marker's Model Theory: An Introduction is a fantastic text as well, but it's better as a second text once you're familiar with some of the basic concepts. $\endgroup$
    – Alex Kocurek
    Commented Jul 28, 2013 at 2:39
  • $\begingroup$ Andres, it is for myself. $\endgroup$
    – Ryan
    Commented Jul 28, 2013 at 2:46
  • $\begingroup$ Alex, thanks for the recommendations. I'm actually going back and forth between the first two you suggested. Do you think one is better than the other? $\endgroup$
    – Ryan
    Commented Jul 28, 2013 at 2:47
  • $\begingroup$ Peter Jipsen did (and posted online) a short course on Universal Algebra for a BLAST conference a few years back. It isn't a royal road to the subject, but as a travelogue and summary it serves well. You might find something similar for Model Theory, which tells you what places to visit and what to look for when you are there. $\endgroup$
    – The Masked Avenger
    Commented Jul 28, 2013 at 6:03

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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.)

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  • $\begingroup$ Thanks Andres. Hodges book sounds good. Unfortunately it's \$268.58. Is there a way to get it cheaper, or is the Shorter Model Theory a close second? $\endgroup$
    – Ryan
    Commented Jul 28, 2013 at 4:59
  • $\begingroup$ (Yes, that is a ridiculous price. I was quite fortunate when I got mine second hand in grad school. I like the short version, but I feel it leaves out much of its substance.) $\endgroup$
    – Andrés E. Caicedo
    Commented Jul 28, 2013 at 5:47
  • $\begingroup$ @Ryan: you can find Hodges' book on bookfi. $\endgroup$
    – Etienne
    Commented Jul 28, 2013 at 22:02

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