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Model theory begins with an audacious idea: to consider statements about mathematical structures as mathematical objects of study in their own right. While inherently important as a tool of mathematical logic, it also enjoys connections to and applications in diverse branches of mathematics, including algebra, number theory and analysis. Despite this, traditional introductions to model theory assume a graduate-level background of the reader. In this innovative textbook, Jonathan Kirby brings model theory to an undergraduate audience. The highlights of basic model theory are illustrated through examples from specific structures familiar from undergraduate mathematics, paying particular attention to definable sets throughout. With numerous exercises of varying difficulty, this is an accessible introduction to model theory and its place in mathematics.
Suitable for use as an undergraduate- or Masters-level course in model theory, unlike traditional graduate-level texts
Contains many exercises of varying difficulty, from bookwork to more substantial projects
Presents model theory in the context of undergraduate mathematics via definable sets in familiar structures
Preface
Part I. Languages and Structures:Index.
Description
Model theory begins with an audacious idea: to consider statements about mathematical structures as mathematical objects of study in their own right. While inherently important as a tool of mathematical logic, it also enjoys connections to and applications in diverse branches of mathematics, including algebra, number theory and analysis. Despite this, traditional introductions to model theory assume a graduate-level background of the reader. In this innovative textbook, Jonathan Kirby brings model theory to an undergraduate audience. The highlights of basic model theory are illustrated through examples from specific structures familiar from undergraduate mathematics, paying particular attention to definable sets throughout. With numerous exercises of varying difficulty, this is an accessible introduction to model theory and its place in mathematics.
Suitable for use as an undergraduate- or Masters-level course in model theory, unlike traditional graduate-level texts
Contains many exercises of varying difficulty, from bookwork to more substantial projects
Presents model theory in the context of undergraduate mathematics via definable sets in familiar structures
