20 citations · 60 across the 13 of their papers we have counts for
14 papers
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…
Symmetry and the Union of Saturated Models in Superstable Abstract Elementary Classes
M. M VanDieren
Our main result (Theorem 1) suggests a possible dividing line (-superstable -symmetric) for abstract elementary classes without using extra set-theoretic assumptions or t…
A Characterization of Uniqueness of Limit Models in Categorical Abstract Elementary Classes
Monica M. VanDieren
In this paper we examine the task set forth by Shelah and Villaveces in \cite{ShVi} of proving the uniqueness of limit models of cardinality in -categorical abstract element…
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…
Limit Models in Strictly Stable Abstract Elementary Classes
Will Boney, Monica M. VanDieren
In this paper, we examine the locality condition for non-splitting and determine the level of uniqueness of limit models that can be recovered in some stable, but not superstable,…