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  1. Toward a Stability Theory of Tame Abstract Elementary Classes.Sebastien Vasey - 2018 - Journal of Mathematical Logic 18 (2):1850009.
    We initiate a systematic investigation of the abstract elementary classes that have amalgamation, satisfy tameness, and are stable in some cardinal. Assuming the singular cardinal hypothesis, we prove a full characterization of the stability cardinals, and connect the stability spectrum with the behavior of saturated models. We deduce that if a class is stable on a tail of cardinals, then it has no long splitting chains. This indicates that there is a clear notion of superstability in this framework. We also (...)
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  • Good Frames in the Hart–Shelah Example.Will Boney & Sebastien Vasey - 2018 - Archive for Mathematical Logic 57 (5-6):687-712.
    For a fixed natural number \, the Hart–Shelah example is an abstract elementary class with amalgamation that is categorical exactly in the infinite cardinals less than or equal to \. We investigate recently-isolated properties of AECs in the setting of this example. We isolate the exact amount of type-shortness holding in the example and show that it has a type-full good \-frame which fails the existence property for uniqueness triples. This gives the first example of such a frame. Along the (...)
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  • Forking in Short and Tame Abstract Elementary Classes.Will Boney & Rami Grossberg - 2017 - Annals of Pure and Applied Logic 168 (8):1517-1551.
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  • Non-Forking W-Good Frames.Marcos Mazari-Armida - forthcoming - Archive for Mathematical Logic:1-26.
    We introduce the notion of a w-good \-frame which is a weakening of Shelah’s notion of a good \-frame. Existence of a w-good \-frame implies existence of a model of size \. Tameness and amalgamation imply extension of a w-good \-frame to larger models. As an application we show:Theorem 0.1. Suppose\. If \ = \mathbb {I} = 1 \le \mathbb {I} < 2^{\lambda ^{++}}\)and\is\\)-tame, then\.The proof presented clarifies some of the details of the main theorem of Shelah and avoids using (...)
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  • Building Independence Relations in Abstract Elementary Classes.Sebastien Vasey - 2016 - Annals of Pure and Applied Logic 167 (11):1029-1092.
  • Saturation and Solvability in Abstract Elementary Classes with Amalgamation.Sebastien Vasey - 2017 - Archive for Mathematical Logic 56 (5-6):671-690.
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  • On the Uniqueness Property of Forking in Abstract Elementary Classes.Sebastien Vasey - 2017 - Mathematical Logic Quarterly 63 (6):598-604.
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  • Building Prime Models in Fully Good Abstract Elementary Classes.Sebastien Vasey - 2017 - Mathematical Logic Quarterly 63 (3-4):193-201.
    We show how to build prime models in classes of saturated models of abstract elementary classes having a well-behaved independence relation: Let math formula be an almost fully good AEC that is categorical in math formula and has the math formula-existence property for domination triples. For any math formula, the class of Galois saturated models of math formula of size λ has prime models over every set of the form math formula. This generalizes an argument of Shelah, who proved the (...)
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  • Superstability From Categoricity in Abstract Elementary Classes.Will Boney, Rami Grossberg, Monica M. VanDieren & Sebastien Vasey - 2017 - Annals of Pure and Applied Logic 168 (7):1383-1395.
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  • Downward Categoricity From a Successor Inside a Good Frame.Sebastien Vasey - 2017 - Annals of Pure and Applied Logic 168 (3):651-692.
  • Shelah's Eventual Categoricity Conjecture in Universal Classes: Part I.Sebastien Vasey - 2017 - Annals of Pure and Applied Logic 168 (9):1609-1642.
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  • Superstability and Symmetry.Monica M. VanDieren - 2016 - Annals of Pure and Applied Logic 167 (12):1171-1183.
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  • Canonical Forking in AECs.Will Boney, Rami Grossberg, Alexei Kolesnikov & Sebastien Vasey - 2016 - Annals of Pure and Applied Logic 167 (7):590-613.
  • Shelah's Eventual Categoricity Conjecture in Tame Abstract Elementary Classes with Primes.Sebastien Vasey - 2018 - Mathematical Logic Quarterly 64 (1-2):25-36.
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