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math.LO2025
Large cardinals beyond HOD
Juan Pablo Aguilera, Joan Bagaria, Gabriel Goldberg +1
Exacting and ultraexacting cardinals are large cardinal numbers compatible with the Zermelo-Fraenkel axioms of set theory, including the Axiom of Choice. In contrast with standard…
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.LO2021
Non-absoluteness of Hjorth's Cardinal Characterization
Philipp Lücke, Ioannis Souldatos
In [5], Hjorth proved that for every countable ordinal , there exists a complete -sentence that has models of all cardinalities less than or equal to…