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math.LO2026
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…
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…