2 papers
math.LO2025
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.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…