2 citations · 2 across the 8 of their papers we have counts for
11 papers
The Cofinality of Generating Familes
Paul Gartside, Thomas Gilton
The topology of a separable metrizable space is \emph{generated} by a family of its subsets provided that a set is closed in if and only if $A\…
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:…
Club Stationary Reflection and other Combinatorial Principles at
Thomas Gilton, Šárka Stejskalová
In this paper we continue the study in [Gilton-Levine-Stejskalova] of compactness and incompactness principles at double successors, focusing here on the case of double successors…
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…
Club Stationary Reflection and the Special Aronszajn Tree Property
Omer Ben-Neria, Thomas Gilton
We prove that it is consistent that Club Stationary Reflection and the Special Aronszajn Tree Property simultaneously hold on , thereby contributing to the study of the tensio…
Abraham-Rubin-Shelah Open Colorings and a Large Continuum
Thomas Gilton, Itay Neeman
We show that the Abraham-Rubin-Shelah Open Coloring Axiom is consistent with a large continuum, in particular, consistent with . This answers one of the main…
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…
The Harrington-Shelah Model with Large Continuum
Thomas Gilton, John Krueger
We prove from the existence of a Mahlo cardinal the consistency of the statement that holds and every stationary subset of reflects to an ordi…
Mitchell's Theorem Revisited
Thomas Gilton, John Krueger
Mitchell's theorem on the approachability ideal states that it is consistent relative to a greatly Mahlo cardinal that there is no stationary subset of …