40 citations · 399 across the 37 of their papers we have counts for
6 papers · 1 filter
On categoricity in successive cardinals
Sebastien Vasey
We investigate, in ZFC, the behavior of abstract elementary classes (AECs) categorical in many successive small cardinals. We prove for example that a universal $\mathbb{L}_{ω_1, ω…
Categoricity and multidimensional diagrams
Saharon Shelah, Sebastien Vasey
We study multidimensional diagrams in independent amalgamation in the framework of abstract elementary classes (AECs). We use them to prove the eventual categoricity conjecture for…
The categoricity spectrum of large abstract elementary classes
Sebastien Vasey
The categoricity spectrum of a class of structures is the collection of cardinals in which the class has a single model up to isomorphism. Assuming that cardinal exponentiation is…
Categoricity in multiuniversal classes
Nathanael Ackerman, Will Boney, Sebastien Vasey
The third author has shown that Shelah's eventual categoricity conjecture holds in universal classes: class of structures closed under isomorphisms, substructures, and unions of ch…
Forking independence from the categorical point of view
Michael Lieberman, Jiří Rosický, Sebastien Vasey
Forking is a central notion of model theory, generalizing linear independence in vector spaces and algebraic independence in fields. We develop the theory of forking in abstract, c…
Structural Logic and Abstract Elementary Classes with Intersection
Will Boney, Sebastien Vasey
We give a syntactic characterization of abstract elementary classes (AECs) closed under intersections using a new logic with a quantifier for isomorphism types that we call structu…