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Klappentext Aimed at research logicians and mathematicians, this much-awaited monograph covers over forty years of work on relative classification theory for non-standard models of arithmetic. With graded exercises at the end of each chapter, the book covers basic isomorphism invariants: families of types realized in a model, lattices of elementary substructures and automorphism groups. Many results involve applications of the powerful technique of minimal types due to Haim Gaifman, and some of the results are classical but have never been published in a book form before. Zusammenfassung Aimed at graduate students and research logicians and mathematicians, this much-awaited text covers over forty years of work on relative classification theory for non-standard models of arithmetic. With graded exercises at the end of each chapter, the book covers basic isomorphism invariants: families of types realized in a model, lattices of elementary substructures and automorphism groups. Many results involve applications of the powerful technique of minimal types due to Haim Gaifman, and some of the results are classical but have never been published in a book form before. Inhaltsverzeichnis Preface 1: Basics 2: Extensions 3: Minimal and other types 4: Substructure lattices 5: How to control types 6: Generics and forcing 7: Cuts 8: Automorphisms of recursively saturated models 9: Automorphism groups of recursively saturated models 10: Omega 1-like models 11: Order types 12: Twenty questions References Index
