3 papers
math.LO2022
PCF Theory and the Tukey Spectrum
Thomas Gilton
In this paper, we investigate the relationship between the Tukey order and PCF theory, as applied to sets of regular cardinals. We show that it is consistent that for all sets …
math.LO2021
Trees and stationary reflection at double successors of regular cardinals
Thomas Gilton, Maxwell Levine, Šárka Stejskalová
We obtain an array of consistency results concerning trees and stationary reflection at double successors of regular cardinals , updating some classical constructions in the pro…
math.LO2019
A note on the eightfold way
Thomas Gilton, John Krueger
Assuming the existence of a Mahlo cardinal, we construct a model in which there exists an -Aronszajn tree, the -approachability property fails, and every stationary subse…