4 citations · 9 across the 14 of their papers we have counts for
15 papers
Model theory of class-sized logics
Jonathan Osinski, Trevor Wilson
We study compactness and Löwenheim-Skolem properties of fragments of the class-sized logic and of class-sized versions of second-order and sort logics…
More Derived Models in PFA
Derek Levinson, Nam Trang, Trevor Wilson
This paper makes significant progress towards resolving a conjecture relating strong forcing axioms like and the derived model at a limit of Woodin cardinals . In particul…
A model of the Axiom of Determinacy in which every set of reals is universally Baire
Paul B. Larson, Grigor Sargsyan, Trevor Wilson
The consistency of the theory ``every set of reals is universally Baire'' is proved relative to ``there is a cardina…
The infinite Fibonacci cube and its generalizations
Hiep Trinh, Trevor M. Wilson
The Fibonacci cube is is the graph whose vertices are independent subsets of the path graph of length , where two such vertices are considered adjacent if they differ by t…
The distinguishing index of graphs with infinite minimum degree
Marcin Stawiski, Trevor M. Wilson
The distinguishing index of a graph is the least number of colors necessary to obtain an edge coloring of that is preserved only by the trivial automorphism. We sho…
Ideals and Strong Axioms of Determinacy
Dominik Adolf, Grigor Sargsyan, Nam Trang +2
We show that the following two theories are equiconsistent: (T) ZFC, CH and "There is a dense ideal on the first uncountable cardinal such that if j is the generic embedding associ…
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…
Weak Vopěnka's Principle does not imply Vopěnka's Principle
Trevor M. Wilson
Vopěnka's Principle says that the category of graphs has no large discrete full subcategory, or equivalently that the category of ordinals cannot be fully embedded into it. Weak Vo…
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…
On forcing projective generic absoluteness from strong cardinals
Trevor M. Wilson
W.H. Woodin showed that if are strong cardinals then two-step generic absoluteness holds after collapsing to be countable. We sh…
Determinacy from strong compactness of
Nam Trang, Trevor Wilson
In the absence of the Axiom of Choice, the "small" cardinal can exhibit properties more usually associated with large cardinals, such as strong compactness and supercompactne…