## A Course in Model TheoryThis concise introduction to model theory begins with standard notions and takes the reader through to more advanced topics such as stability, simplicity and Hrushovski constructions. The authors introduce the classic results, as well as more recent developments in this vibrant area of mathematical logic. Concrete mathematical examples are included throughout to make the concepts easier to follow. The book also contains over 200 exercises, many with solutions, making the book a useful resource for graduate students as well as researchers. |

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### Contents

Elementary extensions and compactness | 17 |

Quantifier elimination | 27 |

Countable models | 47 |

ℵ1categorical theories | 63 |

Morley rank | 89 |

Simple theories | 109 |

Stable theories | 129 |

Prime extensions | 157 |

The fine structure of ℵ1categorical theories | 165 |

Appendix A Set theory | 185 |

Appendix B Fields | 191 |

Combinatorics | 205 |

Solutions to exercises | 213 |

References | 235 |

### Common terms and phrases

0-definable acl(A acleq(A algebraically closed algebraically independent assume atomic automorphism bijection binary tree called canonical parameter choose cl(A closed fields closure complete theory consider consistent construct contains converse Corollary countable models definable deﬁned Definition denote disjoint elementarily equivalent elementary extension elementary map elementary substructure elements embedding equivalence relation Exercise existential extension ofp ﬁnite finite subset finitely satisfiable fork function symbols go(x Hence ifand ifit implies indiscernible induction inﬁnite infinite models isolated isomorphic L-formula L-structure L(A)-formula language Lemma linear order linearly disjoint modular Morley rank Morley sequence MR(a n-tuple n-types non-forking extension notfork ordinal polynomial pregeometry prime extensions prime model procyclic proof of Theorem Proposition prove pseudo-finite quantifier elimination quantifier-free realised relative algebraic saturated saturated model simple theories stable theories strongly minimal strongly minimal set structure SU-rank subgroups totally transcendental theories tuple ultraproduct union unique variables Vaughtian pair X,cl