Superstability and Categoricity in Abstract Elementary Classes, Carnegie Mellon University, USA, 2017. Supervised by Rami Grossberg
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...
متن کاملSuperstability in abstract elementary classes
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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Categoricity and Stability in Abstract Elementary Classes byMonica M. VanDieren This thesis tackles the classification theory of non-elementary classes from twoperspectives. In Chapter II we work towards a categoricity transfer theorem, whileChapter III focuses on the development of a stability theory for abstract elementaryclasses (AECs).The results in Chapter II are in a c...
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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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ELEMENTARY CLASSES RAMI GROSSBERG AND SEBASTIEN VASEY Abstract. In the context of abstract elementary classes (AECs) with a monster model, several possible definitions of superstability have appeared in the literature. Among them are no long splitting chains, uniqueness of limit models, and solvability. Under the assumption that the class is tame and stable, we show that (asymptotically) no lon...
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ژورنال
عنوان ژورنال: The Bulletin of Symbolic Logic
سال: 2018
ISSN: 1079-8986,1943-5894
DOI: 10.1017/bsl.2018.27