40 citations · 399 across the 37 of their papers we have counts for
12 papers · 2 filters
A survey on tame abstract elementary classes
Will Boney, Sebastien Vasey
Tame abstract elementary classes are a broad nonelementary framework for model theory that encompasses several examples of interest. In recent years, progress toward developing a c…
Downward categoricity from a successor inside a good frame
Sebastien Vasey
We use orthogonality calculus to prove a downward transfer from categoricity in a successor in abstract elementary classes (AECs) that have a good frame (a forking-like notion for…
-Abstract Elementary Classes and other generalizations
Will Boney, Rami Grossberg, Michael Lieberman +2
We introduce -Abstract Elementary Classes (-AECs) as a broad framework for model theory that includes complete boolean algebras and Dirichlet series, and begin to develop the…
Building prime models in fully good abstract elementary classes
Sebastien Vasey
We show how to build primes models in classes of saturated models of abstract elementary classes (AECs) having a well-behaved independence relation: Let be…
Shelah's eventual categoricity conjecture in tame AECs with primes
Sebastien Vasey
A new case of Shelah's eventual categoricity conjecture is established: Let be an AEC with amalgamation. Write $H_2 := \beth_{\left(2^{\beth_{\left(2^{\text{…
On the structure of categorical abstract elementary classes with amalgamation
Monica M. VanDieren, Sebastien Vasey
For an abstract elementary class with amalgamation and no maximal models, we show that categoricity in a high-enough cardinal implies structural properties such as the uniquene…
Categoricity and infinitary logics
Will Boney, Sebastien Vasey
We point out a gap in Shelah's proof of the following result: Let be an abstract elementary class categorical in unboundedly many cardinals. Then there exists…
Symmetry in abstract elementary classes with amalgamation
Monica M. VanDieren, Sebastien Vasey
This paper is part of a program initiated by Saharon Shelah to extend the model theory of first order logic to the non-elementary setting of abstract elementary classes (AECs). An…
Equivalent definitions of superstability in tame abstract elementary classes
Rami Grossberg, Sebastien Vasey
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 sp…
Shelah's eventual categoricity conjecture in universal classes: part I
Sebastien Vasey
We prove: Let be a universal class. If is categorical in cardinals of arbitrarily high cofinality, then is categorical on a tail of cardinals. The pr…
Chains of saturated models in AECs
Will Boney, Sebastien Vasey
We study when a union of saturated models is saturated in the framework of tame abstract elementary classes (AECs) with amalgamation. We prove: If is a tame…
Building independence relations in abstract elementary classes
Sebastien Vasey
We study general methods to build forking-like notions in the framework of tame abstract elementary classes (AECs) with amalgamation. We show that whenever such classes are categor…