Classification Theory for Abstract Elementary Classes (Studies in Logic: Mathematical Logic and Foundations)

Shelah, Professor Department Of Mathematics Rutgers University Institute Of Mathematics Saharon

ISBN 10: 1904987710 / ISBN 13: 9781904987710

Published by College Publications, 2009

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Bibliographic Details

• Title: Classification Theory for Abstract Elementary Classes (Studies in Logic: Mathematical Logic and Foundations)
• Publisher: College Publications
• Publication Date: 2009
• Language: English
• ISBN 10: 1904987710
• ISBN 13: 9781904987710
• Binding: Soft cover
• Condition: New

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Synopsis

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.