Classification Theory for Abstract Elementary Classes

Szerző: Saharon Shelah

Nyelv:

Kötés: Puha kötésű

Kiadó: College Publications

Elérhetőség: Beszállítói készleten

Küldés 10-18 napon belül

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An abstract elementary class (AEC) is a class of structures of a fixed vocabulary satisfying some...

Információk a könyvről

Szerző

Saharon Shelah

Nyelv

Angol

Kötés

Könyv - Puha kötésű

Kiadva

2009

oldal

702

EAN

9781904987727

ISBN

9781904987727

Enbook ID

08861632

Kiadó

College Publications

Súly

974

Méretek

236 x 157 x 36

Teljes leírás

An abstract elementary class (AEC) is a class of structures of a fixed vocabulary satisfying some natural closure properties. These classes encompass the normal classes defined in model theory and natural examples arise from mathematical practice, e.g. in algebra not to mention first order and infinitary logics. An AEC is always endowed with a special substructure relation which is not always the obvious one. Abstract elementary classes provide one way out of the cul de sac of the model theory of infinitary languages which arose from over-concentration on syntactic criteria. This is the second volume of a two-volume monograph on abstract elementary classes. It is quite self-contained and deals with three separate issues. The first is the topic of universal classes, i.e. classes of structures of a fixed vocabulary such that a structure belongs to the class if and only if every finitely generated substructure belongs. Then we derive from an assumption on the number of models, the existence of an (almost) good frame. The notion of frame is a natural generalization of the first order concept of superstability to this context. The assumption says that the weak GCH holds for a cardinal $\lambda$, its successor and double successor, and the class is categorical in the first two, and has an intermediate value for the number of models in the third. In particular, we can conclude from this argument the existence of a model in the next cardinal. Lastly we deal with the non-structure part of the topic, that is, getting many non-isomorphic models in the double successor of $ \lambda$ under relevant assumptions, we also deal with almost good frames themselves and some relevant set theory.

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Classification Theory for Abstract Elementary Classes

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