40 citations · 136 across the 24 of their papers we have counts for
10 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…
No Maximal Models from Looking Down
Will Boney
In [Sh893], Shelah proves that (on a stationary set of cardinals) an AEC has not too many models or every model has extensions of arbitrary cardinality. We show that, if we assume…
Hanf Numbers and Presentation Theorems in AECs
Will Boney, John Baldwin
We prove that a strongly compact cardinal is an upper bound for a Hanf number for amalgamation, etc. in AECs using both semantic and syntactic methods. To syntactically prove non-d…
The Γ-Ultraproduct and Averageable Classes
Will Boney
We consider an ultraproduct that is designed to omit a fixed set of unary types , called the -ultraproduct. The -ultraproduct is not always well-behaved, but we discuss se…
-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…
Large Cardinal Axioms from Tameness in AECs
Will Boney, Spencer Unger
We show that various tameness assertions about abstract elementary classes imply the existence of large cardinals under mild cardinal arithmetic assumptions.
Around the set-theoretical consistency of d-tameness of Metric Abstract Elementary Classes
Will Boney, Pedro Zambrano
In this paper, we prove that if is a almost strongly compact cardinal, then any MAEC with Löwenheim-Skolem number below is -d-tame.
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,…
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…
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…