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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Classification Theory for Abstract Elementary Classes

Classification Theory for Abstract Elementary Classes

Shelah, Saharon

Paperback

Series: Studies in Logic: Mathematical Logic and Foundations

FictionGeneral Computers

ISBN10: 1904987710
ISBN13: 9781904987710
Publisher: Kings College Pubn
Published: Apr 24 2009
Pages: 824
Weight: 2.49
Height: 1.63 Width: 6.14 Depth: 9.21
Language: English
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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