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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.LO2023
Intrinsic Justification for Large Cardinals and Structural Reflection
Joan Bagaria, Claudio Ternullo
We deal with the complex issue of whether large cardinals are intrinsically justified principles of set theory (we call this the Intrinsicness Issue). In order to do this, we revie…
math.LO2015
On partial orderings having precalibre- and fragments of Martin's axiom
Joan Bagaria, Saharon Shelah
We define a countable antichain condition (ccc) property for partial orderings, weaker than precalibre-, and show that Martin's axiom restricted to the class of partial o…