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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 logics…
math.LO2025
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.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…