Classification Theory for Abstract Elementary Classes

Shelah, Saharon

ISBN 10: 1904987710 ISBN 13: 9781904987710

Verlag: College Publications, 2009

Sprache: Englisch

Zustand: Neu Softcover

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Bibliografische Details

Titel

Classification Theory for Abstract Elementary Classes

Verlag

College Publications

Erscheinungsjahr

2009

Sprache

Englisch

ISBN-10

1904987710

ISBN-13

9781904987710

Einband

Softcover

Zustand

New

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�ber diesen Titel

Inhaltsangabe

An abstract elementary class is a class of structures of the same vocabulary (like a class of rings, or a class of fields), with a partial order that generalizes the relation "A is a substructure (or an elementary substructure) of B". The requirements are that the class is closed under isomorphism, and that isomorphic structures have isomorphic (generalized) substructures; we also require that our classes share some of the most basic properties of elementary classes, like closure under unions of increasing chains of substructures.We would like to classify this general family; in the sense of proving dichotomies: either we can understand the structure of all models in our class or there are many to some extent. More specifically we would like to generalize the theory about categoricity and superstability to this context.

Rese�a del editor

An abstract elementary class is a class of structures of the same vocabulary (like a class of rings, or a class of fields), with a partial order that generalizes the relation "A is a substructure (or an elementary substructure) of B". The requirements are that the class is closed under isomorphism, and that isomorphic structures have isomorphic (generalized) substructures; we also require that our classes share some of the most basic properties of elementary classes, like closure under unions of increasing chains of substructures. We would like to classify this general family; in the sense of proving dichotomies: either we can understand the structure of all models in our class or there are many to some extent. More specifically we would like to generalize the theory about categoricity and superstability to this context.

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