Classification of δ-invariant amalgamation classes
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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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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In abstract elementary classes limit models are sometimes the appropriate substitute for saturated models. For Galois-stable abstract elementary classes which satisfy the amalgamation property, we prove under the assumption that there is a mildly behaved dependence relation, that for any model M , any two limit models over M of the same cardinality are isomorphic. This is useful in dealing with...
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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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We introduce an abstract class of algebras that is a proper reduct of both Pinter’s substitution algebras and cylindric algebras. We show that the class of representable algebras have the amalgamation property. Pinter’s substitution algebras were introduced by Pinter [13], [14]. Such algebras are obtained from cylindric algebras by dropping the diagonal elements and adding unary operations of s...
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ژورنال
عنوان ژورنال: Journal of Symbolic Logic
سال: 1999
ISSN: 0022-4812,1943-5886
DOI: 10.2307/2586809