An Invitation to Model Theory

Description

In this innovative and largely self-contained 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, and numerous exercises of varying difficulty further consolidate the student's learning. Contents Preface PART I LANGUAGES AND STRUCTURES 1 Structures 2 Terms 3 Formulas 4 Definable Sets 5 Substructures and Quantifiers PART II THEORIES AND COMPACTNESS 6 Theories and Axioms 7 The Complex and Real Fields 8 Compactness and New Constants 9 Axiomatisable Classes 10 Cardinality Considerations 11 Constructing Models from Syntax PART III CHANGING MODELS 12 Elementary Substructures 13 Elementary Extensions 14 Vector Spaces and Categoricity 15 Linear Orders 16 The Successor Structure PART IV CHARACTERISING DEFINABLE SETS 17 Quantifier Elimination for DLO 18 Substructure Completeness 19 Power Sets and Boolean Algebras 20 The Algebras of Definable Sets 21 Real Vector Spaces and Parameters 22 Semi-algebraic Sets PART V TYPES 23 Realising Types 24 Omitting Types 25 Countable Categoricity 26 Large and Small Countable Models 27 Saturated Models PART VI ALGEBRAICALLY CLOSED FIELDS 28 Fields and Their Extensions 29 Algebraic Closures of Fields 30 Categoricity and Completeness 31 Definable Sets and Varieties 32 Hilbert’s Nullstellensatz Bibliography Index