40 citations · 399 across the 37 of their papers we have counts for
8 papers · 2 filters
On the uniqueness property of forking in abstract elementary classes
Sebastien Vasey
In the setup of abstract elementary classes satisfying a local version of superstability, we prove the uniqueness property for -forking, a certain independence notion arising fr…
Quasiminimal abstract elementary classes
Sebastien Vasey
We propose the notion of a quasiminimal abstract elementary class (AEC). This is an AEC satisfying four semantic conditions: countable Löwenheim-Skolem-Tarski number, existence of…
Shelah-Villaveces revisited
Will Boney, Monica M. VanDieren, Sebastien Vasey
We study uniqueness of limit models in abstract elementary classes (AECs) with no maximal models. We prove (assuming instances of diamonds) that categoricity in a cardinal of the f…
Superstability from categoricity in abstract elementary classes
Will Boney, Rami Grossberg, Monica M. VanDieren +1
Starting from an abstract elementary class with no maximal models, Shelah and Villaveces have shown (assuming instances of diamond) that categoricity implies a superstability-like…
Toward a stability theory of tame abstract elementary classes
Sebastien Vasey
We initiate a systematic investigation of the abstract elementary classes that have amalgamation, satisfy tameness (a locality property for orbital types), and are stable (in terms…
Good Frames in the Hart-Shelah Example
Will Boney, Sebastien Vasey
For a fixed natural number , the Hart-Shelah example is an abstract elementary class (AEC) with amalgamation that is categorical exactly in the infinite cardinals less th…