5 papers
Compactness beyond choice and HOD
Jonathan Osinski
We characterise exacting, rank-Berkeley, Berkeley, and club Berkeley cardinals by compactness properties of logics and, equivalently, by compactness properties of certain topologic…
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…
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…
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…
Upward Löwenheim-Skolem-Tarski Numbers for Abstract Logics
Victoria Gitman, Jonathan Osinski
Galeotti, Khomskii and Väänäanen recently introduced the notion of the upward Löwenheim-Skolem-Tarski number for a logic, strengthening the classical notion of a Hanf number. A car…