17 found
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  1.  4
    Forking and Superstability in Tame Aecs.Sebastien Vasey - 2016 - Journal of Symbolic Logic 81 (1):357-383.
  2.  8
    Building Independence Relations in Abstract Elementary Classes.Sebastien Vasey - 2016 - Annals of Pure and Applied Logic 167 (11):1029-1092.
  3.  2
    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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  4.  6
    Canonical Forking in AECs.Will Boney, Rami Grossberg, Alexei Kolesnikov & Sebastien Vasey - 2016 - Annals of Pure and Applied Logic 167 (7):590-613.
  5.  5
    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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  6.  7
    Downward Categoricity From a Successor Inside a Good Frame.Sebastien Vasey - 2017 - Annals of Pure and Applied Logic 168 (3):651-692.
  7.  4
    Universal Classes Near ${\Aleph _1}$.Marcos Mazari-Armida & Sebastien Vasey - 2018 - Journal of Symbolic Logic 83 (4):1633-1643.
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  8.  7
    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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  9.  8
    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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  10.  7
    Abstract Elementary Classes Stable in ℵ 0.Saharon Shelah & Sebastien Vasey - 2018 - Annals of Pure and Applied Logic 169 (7):565-587.
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  11.  3
    Quasiminimal Abstract Elementary Classes.Sebastien Vasey - 2018 - Archive for Mathematical Logic 57 (3-4):299-315.
    We propose the notion of a quasiminimal abstract elementary class. This is an AEC satisfying four semantic conditions: countable Löwenheim–Skolem–Tarski number, existence of a prime model, closure under intersections, and uniqueness of the generic orbital type over every countable model. We exhibit a correspondence between Zilber’s quasiminimal pregeometry classes and quasiminimal AECs: any quasiminimal pregeometry class induces a quasiminimal AEC, and for any quasiminimal AEC there is a natural functorial expansion that induces a quasiminimal pregeometry class. We show in particular (...)
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  12.  5
    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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  13.  14
    Indiscernible Extraction and Morley Sequences.Sebastien Vasey - 2017 - Notre Dame Journal of Formal Logic 58 (1):127-132.
    We present a new proof of the existence of Morley sequences in simple theories. We avoid using the Erdős–Rado theorem and instead use only Ramsey’s theorem and compactness. The proof shows that the basic theory of forking in simple theories can be developed using only principles from “ordinary mathematics,” answering a question of Grossberg, Iovino, and Lessmann, as well as a question of Baldwin.
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  14.  5
    On the Uniqueness Property of Forking in Abstract Elementary Classes.Sebastien Vasey - 2017 - Mathematical Logic Quarterly 63 (6):598-604.
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  15.  5
    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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  16.  2
    Superstability and Categoricity in Abstract Elementary Classes, Carnegie Mellon University, USA, 2017. Supervised by Rami Grossberg.Christian Rosendal & Sebastien Vasey - 2018 - Bulletin of Symbolic Logic 24 (2):192-194.
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  17.  2
    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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