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math.LO2024
Large cardinals, structural reflection, and the HOD Conjecture
Juan P. Aguilera, Joan Bagaria, Philipp Lücke
We introduce exacting cardinals and a strengthening of these, ultraexacting cardinals. These are natural large cardinals defined equivalently as weak forms of rank-Berkeley cardina…
math.LO2024
The complexity of non-stationary ideals
Philipp Lücke
We present an overview of results on the question of whether the non-stationary ideal of an uncountable regular cardinal can be defined by a -formula using parameters of h…
math.LO2024
Outward compactness
Peter Holy, Philipp Lücke, Sandra Müller
We introduce and study a new type of compactness principle for strong logics that, roughly speaking, infers the consistency of a theory from the consistency of its small fragments…