Model Theory An Introduction [Paperback]

Assumes only a familiarity with algebra at the beginning graduate level; Stresses applications to algebra; Illustrates several of the ways Model Theory can be a useful tool in analyzing classical mathematical structuresIntroduction * Structures and Theories * Basic Techniques * Algebraic Examples * Realizing and Omitting Types * Indiscernibles * w-stable theoryes * w-stable groups * Geometry of strongly minmal sets * Appendix A: Set Theory * Appendix B: Real Algebra * References * Index

From the reviews:

MATHEMATICAL REVIEWS

This is an extremely fine graduate level textbook on model theory. There is a careful selection of topics&There is a strong focus on the meaning of model-theoretic concepts in mathematically interesting examples. The exercises touch on a wealth of beautiful topics.

This is an extremely fine graduate level textbook on model theory. There is a careful selection of topics, with a route leading to a substantial treatment of Hrushovskis proof of the Mordell-Lang conjecture for function fields. & The exercises touch on a wealth of beautiful topics. & There is additional basic background in two appendices (on set theory and on real algebra). (Dugald Macpherson, Mathematical Reviews, 2003 e)

Model theory is the branch of mathematical logic that examines what it means for a first-order sentence & to be true in a particular structure & . This is a text for graduate students, mainly aimed at those specializing in logic, but also of interest for mathematicians outside logic who want to know what model theory can offer them in their own disciplines. & it is one which makes a good case for model theory as much more than a tool for specialist logicians. (Gerry Leversha, The Mathematical Gazette, Vol. 88 (513), 2004)

The authors intended audience for this high level introduction to model theory is graduate students contemplating research in model theory, gl“'