3 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
Model theory of class-sized logics
Jonathan Osinski, Trevor Wilson
We study compactness and Löwenheim-Skolem properties of fragments of the class-sized logic and of class-sized versions of second-order and sort logic…
math.LO2024
On the optimality of the HOD dichotomy
Gabriel Goldberg, Jonathan Osinski, Alejandro Poveda
In the first part of the manuscript, we establish several consistency results concerning Woodin's $\HOD$ hypothesis and large cardinals around the level of extendibility. First, we…