Research

• Comparing various club guessing principles*, in preparation.
• The precipitousness of tail club guessing ideals*, submitted (PDF)
• Club guessing sequences - Natural structures in set theory - (Japanese)*, submitted to Sugaku.
• Notes on sub-Ostaszewski spaces*, accepted. (PDF)
• A non $D$-space with large extent*, Topology and Its Applications 155(11)(2008), 1256-1263. (Science Direct)
• Mimimality of non $\sigma$-scattered orders (with Justin Moore), accepted. (PDF)
• A fine structure construction of a perfectly normal, non-realcompact space, Topology Proceedings 30(2) (2006), 533-545
• The saturation of club guessing ideals, Annals of Pure and Applied Logic 142(1-3)(2006), 398-424. (Science Direct)
• A tail club guessing ideal can be saturated without being a restriction of the non-stationary ideal, The Notre Dame Journal of Formal Logic, 46(3)(2005), 327--333. (Project Euclid)
• More on perfectly normal, non-realcompact spaces, Topology and Its Applications 153(9)(2006), 1476--1499. (Science Direct)
• $\alpha$-properness and Axiom A, Fundamenta Mathematicae, 186(2005), 25--37. (IMPAN)
• Club guessing sequences and filters, Journal of Symbolic Logic, 70(4)(2005), 1037--1071. (Project Euclid)
• A perfectly normal nonrealcompact space consistent with $\mathsf{MA}_{\aleph_{1}} (with Fernando Hernández-Hernández), Topology and Its Applications, 143(1--3)(2004), 175--188. (Science Direct)
• Directive trees and games on posets (with Yasuo Yoshinobu), Proceedings of the American Mathematical Society, 130(2002), 1477--1485. (AMS)

• The weak diamond*(PDF) - the proof of "$2^{\aleph_0}<2^{\aleph_1}$ implies the weak diamond", (hopefully easier to read than the paper of Devlin and Shelah)

• A precipitous club guessing ideal on omega_1* (ESI workshop), ESI workshop on large cardinals and descriptive set theory, June, 2009
• The principle $(+)$ and club guessing sequences* (PDF), Boise Extravaganza in Set Theory at Boise State University, March 2008
• The comparison of various club guessing principles* (PDF), BLAST at University of Denver, August 2008

The above entries marked with a * are subject to the following acknowledgment and disclaimer:
This material is based upon work supported by the National Science Foundation under Grant No.~0700983.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.