7 papers · 1 filter
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…
A game-theoretic proof of Shelah's theorem on labeled trees
Trevor M. Wilson
We give a new proof of a theorem of Shelah which states that for every family of labeled trees, if the cardinality of the family is much larger (in the sense of large cardinals…
The large cardinal strength of Weak Vopěnka's Principle
Trevor M. Wilson
We show that Weak Vopěnka's Principle, which is the statement that the opposite category of ordinals cannot be fully embedded into the category of graphs, is equivalent to the larg…
The consistency strength of the perfect set property for universally Baire sets of reals
Ralf Schindler, Trevor M. Wilson
We show that the statement "every universally Baire set of reals has the perfect set property" is equiconsistent modulo ZFC with the existence of a cardinal that we call a virtuall…
Generic Vopěnka cardinals and models of ZF with few -Suslin sets
Trevor M. Wilson
We define a generic Vopěnka cardinal to be an inaccessible cardinal such that for every first-order language of cardinality less than and every set $\mathscr{…
Weakly remarkable cardinals, Erdős cardinals, and the generic Vopěnka principle
Trevor M. Wilson
We consider a weak version of Schindler's remarkable cardinals that may fail to be -reflecting. We show that the -reflecting weakly remarkable cardinals are exactly the r…