collaborators

5 papers

math.LO2026

Model-theoretic characterizations of large cardinals (Re)visited

Will Boney, Jonathan Osinski

We characterize several large cardinal notions by model-theoretic properties of extensions of first-order logic. We show that -strong cardinals, and, as a corollary, ``Ord is…

math.LO2026

Erdős-Rado Classes

Will Boney

We amalgamate two generalizations of Ramsey's Theorem--Ramsey classes and the Erdős-Rado Theorem--into the notion of a combinatorial Erdős-Rado class. These classes are closely r…

math.LO2026

Definable Coherent Ultrapowers and Elementary Extensions

Will Boney

We develop the notion of coherent ultrafilters (extenders without normality or well-foundedness). We then use definable coherent ultraproducts to characterize any extension of a mo…

math.LO2026

-Stationary logic as an -Abstract Elementary Class

Will Boney

-Abstract Elementary Classes are a model theoretic framework introduced in [BGL+16] to encompass classes axiomatized by . We show that the framewor…

math.LO2025

A Module-theoretic Introduction to Abstract Elementary Classes

Will Boney

The first-order model theory of modules has been studied for decades. More recently, the model theoretic study of nonelementary classes of modules--especially Abstract Elementary C…