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  1. A Topology for Galois Types in Abstract Elementary Classes.Michael Lieberman - 2011 - Mathematical Logic Quarterly 57 (2):204-216.
    We present a way of topologizing sets of Galois types over structures in abstract elementary classes with amalgamation. In the elementary case, the topologies thus produced refine the syntactic topologies familiar from first order logic. We exhibit a number of natural correspondences between the model-theoretic properties of classes and their constituent models and the topological properties of the associated spaces. Tameness of Galois types, in particular, emerges as a topological separation principle. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
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  • Building Independence Relations in Abstract Elementary Classes.Sebastien Vasey - 2016 - Annals of Pure and Applied Logic 167 (11):1029-1092.
  • 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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  • 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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  • 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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  • The Small Index Property for Homogeneous Models in AEC's.Zaniar Ghadernezhad & Andrés Villaveces - 2018 - Archive for Mathematical Logic 57 (1-2):141-157.
    We prove a version of a small index property theorem for strong amalgamation classes. Our result builds on an earlier theorem by Lascar and Shelah. We then study versions of the small index property for various non-elementary classes. In particular, we obtain the small index property for quasiminimal pregeometry structures.
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  • Tameness and Extending Frames.Will Boney - 2014 - Journal of Mathematical Logic 14 (2):1450007.