Superstability from categoricity in abstract elementary classes
نویسندگان
چکیده
منابع مشابه
Superstability from categoricity in abstract elementary classes
Starting from an abstract elementary class with no maximal models, Shelah and Villaveces have shown (assuming instances of diamond) that categoricity implies a superstability-like property for nonsplitting, a particular notion of independence. We generalize their result as follows: given any abstract notion of independence for Galois (orbital) types over models, we derive that the notion satisf...
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We prove that several definitions of superstability in abstract elementary classes (AECs) are equivalent under the assumption that the class is stable, tame, has amalgamation, joint embedding, and arbitrarily large models. This partially answers questions of Shelah. Theorem 0.1. Let K be a tame AEC with amalgamation, joint embedding, and arbitrarily large models. Assume K is stable. Then the fo...
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Metric Abstract Elementary Classes (MAECs) correspond to an amalgam of the notions of Abstract Elementary Classes (AECs) and Elementary Class in the Continuous Logic. In this work, we study a proof of uniqueness (up to isomorphism) of Limit Models in MAECs [ViZa10a, Za1x], under superstability-like assumptions. Assuming this uniqueness of Limit Models, it is possible to do a preliminar study of...
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We prove that from categoricity in λ we can get categoricity in all cardinals ≥ λ in a χ-tame abstract elementary classe K which has arbitrarily large models and satisfies the amalgamation and joint embedding properties, provided λ > LS(K) and λ ≥ χ. For the missing case when λ = LS(K), we prove that K is totally categorical provided that K is categorical in LS(K) and LS(K).
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2017
ISSN: 0168-0072
DOI: 10.1016/j.apal.2017.01.005