Thomas Gilton

Visiting Assistant Professor
Department of Mathematics, University of Pittsburgh

Thackeray 622
Email: tdg25 "at" pitt "dot" edu

My research is in mathematical logic and set theory. More specifically, I focus on using the technique of Forcing to prove that various combinatorial principles are consistent with ZFC Set Theory. I focus on generalizations of Ramsey's Theorem to the uncountable obtained by putting topological restraints on the colorings, as well as on various compactness and incompactness principles that measure how close a model of set theory is to Godel's Constructible Universe. Many of the latter involve Large Cardinals.

Publication List

(In reverse chronological order)

EBFs, Club Stationary Reflection, and the Tree Property
In Progress
PCF Theory and the Tukey Spectrum
Submitted
pdf
Club Stationary Reflection and Other Combinatorial Principles at aleph_{omega+2} (with Sarka Stejskalova)
Submitted
pdf
Club Stationary Reflection and the Special Aronszajn Tree Property (with Omer Ben-Neria)
Canadian Journal of Mathematics.
pdf
Trees and Stationary Reflection at Double Successors of Regular Cardinals (with Maxwell Levine and Sarka Stejskalova)
Journal of Symbolic Logic, 2022
pdf
Abraham-Rubin-Shelah Open Colorings and a Large Continuum (with Itay Neeman)
Journal of Mathematical Logic, vol. 22 (2022), article number 2150027, 55 pages
pdf
A Note on the Eightfold Way (with John Krueger)
Proceedings of the American Mathematical Society 148 (2020), no. 3, 1283-1293
pdf
Side Conditions and Iteration Theorems (with Itay Neeman)
From the 2016 Appalachian Set Theory conference.
To appear in the next AST volume.
pdf
The Harrington-Shelah Model with a Large Continuum (with John Krueger)
Journal of Symbolic Logic 84 (2019), no. 2, 684-703
pdf
Mitchell's Theorem Revisited (with John Krueger)
Annals of Pure and Applied Logic Volume 168 (2017), no. 5, pp 922-1016
pdf

Other Writing

For a copy of my Ph.D. thesis, go here. For a copy of my CV, go here