Overview

This book offers an introductory course in model theory emphasizing connections to algebra. It will be an appropriate introduction both for graduate students interested in advanced work in model theory and for students and researchers in logic or algebra who want to learn the basic results and themes of model theory. In the end, the reader will have a firm background in model theory and be well motivated and well prepared for more advanced treatments like Pillay's ""Geometric Model Theory"" or Buechler's ""Essential Stability Theory. ""While some familiarity at the undergraduate level with mathematical logic would be helpful, it is not assumed. The author assumes familiarity with algebra at the first-year graduate level.

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Reviews

"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 Hrushovski’s 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 author’s intended audience for this high level introduction to model theory is graduate students contemplating research in model theory, graduate students in logic, and mathematicians who are not logicians but who are in areas where model theory has interesting applications. … The text is noteworthy for its wealth of examples and its desire to bring the student to the point where the frontiers of research are visible. … this book should be on the shelf of anybody with an interest in model theory."" (J. M. Plotkin, Zentralblatt Math, Vol. 1003 (03), 2003)"

From the reviews: <p>MATHEMATICAL REVIEWS <p> This is an extremely fine graduate level textbook on model theory. There is a careful selection of topicsa ]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. <p> 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 Hrushovskia (TM)s proof of the Mordell-Lang conjecture for function fields. a ] The exercises touch on a wealth of beautiful topics. a ] There is additional basic background in two appendices (on set theory and on real algebra). (Dugald Macpherson, Mathematical Reviews, 2003 e) <p> Model theory is the branch of mathematical logic that examines what it means for a first-order sentence a ] to be true in a particular structure a ] . 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. a ] 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) <p> The authora (TM)s intended audience for this high level introduction to model theory is graduate students contemplating research in model theory, graduate students in logic, and mathematicians who are not logicians but who are in areas where model theory has interesting applications. a ] The text is noteworthy for its wealth of examples and its desire to bring the student to the point where the frontiers ofresearch are visible. a ] this book should be on the shelf of anybody with an interest in model theory. (J. M. Plotkin, Zentralblatt Math, Vol. 1003 (03), 2003)

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 Hrushovski's 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 author's intended audience for this high level introduction to model theory is graduate students contemplating research in model theory, graduate students in logic, and mathematicians who are not logicians but who are in areas where model theory has interesting applications. ... The text is noteworthy for its wealth of examples and its desire to bring the student to the point where the frontiers of research are visible. ... this book should be on the shelf of anybody with an interest in model theory. (J. M. Plotkin, Zentralblatt Math, Vol. 1003 (03), 2003)

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