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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…
math.LO2024
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…