## A Guide to Classical and Modern Model TheorySince its birth, Model Theory has been developing a number of methods and concepts that have their intrinsic relevance, but also provide fruitful and notable applications in various fields of Mathematics. It is a lively and fertile research area which deserves the attention of the mathematical world. This volume-is easily accessible to young people and mathematicians unfamiliar with logic; -gives a terse historical picture of Model Theory; -introduces the latest developments in the area; -provides 'hands-on' proofs of elimination of quantifiers, elimination of imaginaries and other relevant matters. A Guide to Classical and Modern Model Theory is for trainees and professional model theorists, mathematicians working in Algebra and Geometry and young people with a basic knowledge of logic. |

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### Contents

Structures | 1 |

Quantifier Elimination | 43 |

Model Completeness | 85 |

Elimination of imaginaries | 121 |

Morley rank | 133 |

ω stability | 181 |

Classifying | 221 |

Model Theory and Algebraic Geometry | 291 |

Ominimality | 313 |

### Other editions - View all

A Guide to Classical and Modern Model Theory Annalisa Marcja,Carlo Toffalori No preview available - 2011 |

### Common terms and phrases

0-definable Accordingly acl(X algebraically closed fields assume automorphism cardinal Chapter classification closure Compactness complete theory Conjecture consequently Corollary countable DCFo decomposition deduce definable sets definable subsets Definition denote dense linear orders differential field differentially closed fields domain elementarily equivalent elementary function elementary substructure elements embedding endpoints enlarge examples existentially closed exists extension fact fields of characteristic finite union formula p(v framework hence implies infinite intervals irreducible isolated isomorphism L-formula L(X)-formula language Lemma model completeness Model Theory Morley degree Morley rank n-type non-algebraic Notice notion o-minimal structure ordered field ordinal parameters particular pointwise positive integer pp-formulas prime models Proof quantifier elimination quantifier free formula real closed field realize recall relation RM(p RM(X satisfying saturated model sentences sequence Shelah's small subset strongly minimal subfield subgroup symbol Theorem tuple uncountable unique vectorspaces w-stable group w-stable theories Zariski