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An invitation to model theory / Jonathan Kirby, University of East Anglia.

by Kirby, Jonathan, 1979- author.

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Cambridge, United Kingdom : Cambridge University Press, 2019.

9781107163881 (hardback ; alk. paper)

1107163889 (hardback ; alk. paper)

9781316615553 (pbk. ; alk. paper) :

1316615553 (pbk. ; alk. paper)

xiii, 182 pages : illustrations ; 23 cm

Structures -- Terms -- Formulas -- Definable sets -- Substructures and quantifiers -- Theories and axioms -- The complex and real fields -- Compactness and new constants -- Axiomatisable classes -- Cardinality considerations -- Constructing models from syntax -- Elementary substructures -- Elementary extensions -- Vector spaces and categoricity -- Linear orders -- The successor structure -- Quantifier elimination for DLO -- Substructure completeness -- Power sets and boolean algebras -- The algebras of definable sets -- Real vector spaces and parameters -- Semi-algebraic sets -- Realising types -- Omitting types -- Countable categoricity -- Large and small countable models -- Saturated models -- Fields and their extensions -- Algebraic closures of fields -- Categoricity and completeness -- Definable sets and varieties -- Hilbert's nullstellensatz.

"This book is designed as an undergraduate or masters level course in model theory. It has grown out of courses taught for many years in Oxford, and courses taught by me at UEA. The choice of material and presentation is based on pedagogical considerations, and I have tried to resist the temptation to be encyclopedic. In this book, the main programme of model theory is to take a familiar mathematical structure and get an understanding of it in the following way. First, find an axiomatisation of its complete theory"--

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