5 papers · 1 filter
Forcing Axioms for Proper Posets Preserving a Topological Property: Consistency Results
Thomas Gilton
Forcing axioms are generalizations of Baire category principles that allow one to intersect more dense open sets and to do so in a wider variety of circumstances. In this paper we…
Preservation of Topological Properties by Strongly Proper Forcings
Thomas Gilton, Jared Holshouser
In this paper we show that forcings which are strongly proper for stationarily many countable elementary submodels preserve each of the following properties of topological spaces:…
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 …
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…
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…