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You can find lots of other applications just by browsing the titles of the papers on the MODNET preprint server (follow this link and look under "Publications" on the left side of the page). For example:

  1. "The monomorphism problem in free groups", by L. Ciobanu and A. Ould Houcine (in which they show it is decidable);

  2. "An invitation to model-theoretic Galois theory," by A. Medvedev and Ramin Takloo-Bighash -- expository paper explaining how the Galois correspondence can be explained using model theoretic tools;

  3. "On algebraic closure in pseudofinite fields," by O. Beyarslan and E. Hrushovski;

etc.

Also, there is a recent book Model Theory with Applications to Algebra and Analysis: v. 1 (LMS Lecture Note series v. 349, Cambridge, 2008) which would probably be very relevant (judging by the table of contents -- unfortunately I haven't had a chance to read it yet).
show/hide this revision's text 1

You can find lots of other applications just by browsing the titles of the papers on the MODNET preprint server. For example:

  1. "The monomorphism problem in free groups", by L. Ciobanu and A. Ould Houcine (in which they show it is decidable);

  2. "An invitation to model-theoretic Galois theory," by A. Medvedev and Ramin Takloo-Bighash -- expository paper explaining how the Galois correspondence can be explained using model theoretic tools;

  3. "On algebraic closure in pseudofinite fields," by O. Beyarslan and E. Hrushovski;

etc.

Also, there is a recent book Model Theory with Applications to Algebra and Analysis: v. 1 (LMS Lecture Note series v. 349, Cambridge, 2008) which would probably be very relevant (judging by the table of contents -- unfortunately I haven't had a chance to read it yet).