Symmetry in abstract elementary classes with amalgamation
نویسندگان
چکیده
منابع مشابه
Symmetry in abstract elementary classes with amalgamation
This paper is part of a program initiated by Saharon Shelah to extend the model theory of first order logic to the nonelementary setting of abstract elementary classes (AECs). An abstract elementary class is a semantic generalization of the class of models of a complete first order theory with the elementary substructure relation. We examine the symmetry property of splitting (previously isolat...
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Theorem 0.1. Let K be an abstract elementary class (AEC) with amalgamation and no maximal models. Let λ > LS(K). If K is categorical in λ, then the model of cardinality λ is Galois-saturated. This answers a question asked independently by Baldwin and Shelah. We deduce several corollaries: K has a unique limit model in each cardinal below λ, (when λ is big-enough) K is weakly tame below λ, and t...
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For K an abstract elementary class with amalgamation and no maximal models, we show that categoricity in a highenough cardinal implies structural properties such as the uniqueness of limit models and the existence of good frames. This improves several classical results of Shelah. Theorem 0.1. Let μ ≥ LS(K). If K is categorical in a λ ≥ i(2μ)+ , then: (1) Whenever M0,M1,M2 ∈ Kμ are such that M1 ...
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Let K be an abstract elementary class with amalgamation, and Lowenheim Skolem number LS(K). We prove that for a suitable Hanf number χ0 if χ0 < λ0 ≤ λ1, and K is categorical in λ + 1 then it is categorical in λ0. 2000 Mathematics Subject Classification. 03C45, 03C75.
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ژورنال
عنوان ژورنال: Archive for Mathematical Logic
سال: 2017
ISSN: 0933-5846,1432-0665
DOI: 10.1007/s00153-017-0533-z