1 citations · 3 across the 12 of their papers we have counts for
13 papers
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…
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…
Patterns of Structural Reflection in the large-cardinal hierarchy
Joan Bagaria, Philipp Lücke
We unveil new patterns of Structural Reflection in the large-cardinal hierarchy below the first measurable cardinal. Namely, we give two different characterizations of strongly unf…
Large cardinals as principles of Structural Reflection
Joan Bagaria
After discussing the limitations inherent to all set-theoretic reflection principles akin to those studied by A. Lévy et. al. in the 1960's, we introduce new principles of reflecti…
Huge Reflection
Joan Bagaria, Philipp Lücke
We study Structural Reflection beyond Vopěnka's Principle, at the level of almost-huge cardinals and higher, up to rank-into-rank embeddings. We identify and classify new large car…
The Weak Vopěnka Principle for definable classes of structures
Joan Bagaria, Trevor Wilson
We give a level-by-level analysis of the Weak Vopěnka Principle for definable classes of relational structures (WVP), in accordance with the complexity of their definition, and we…