Research Interests

My research interests mainly fall under the broad category of Logic and Foundations of Mathematics. Specifically, I do research in Set Theory, Boolean Algebras, and Recursion Theory, with a bit of Measure Theory. I have investigated relationships between random reals, eventually dominating functions, measure, generalized weak distributive laws, infinitary two-player games, and complete embeddings of the Cohen algebra into complete Boolean algebras. Currently, I am working on problems on iterated forcing and large cardinals, as well as some problems in Boolean algebras.

Papers

"Generalized weak distributive laws in Boolean algebras and issues related to a problem of von Neumann" thesis.dvi, thesis.ps, thesis.pdf

"Games and general distributive laws in Boolean algebras," Proc. Amer. Math. Soc. 131 (2003) 309-318.

"Errata to `Games and general distributive laws in Boolean algebras'," Proc. Amer. Math. Soc. 131 (2003) 2967-2968.

"Complete embeddings of the Cohen algebra into three families of c.c.c., non-measurable Boolean algebras," Pacific Jour. Math. 214(2) (2004) 201-222.

Book Review: Herbert B. Enderton. "A Mathematical Introduction to Logic," Bull. Symbolic Logic. 9(3) (2003) 406-407.

(Joint with Stephen G. Simpson) "Almost everywhere domination," Jour. of Symbolic Logic 69(3) (2004) 914-922.

(Joint with Sy-David Friedman) "Co-stationarity of the ground model," Jour. Symbolic Logic 71(3) (2006) 1029-1043. co-stationarity.dvi, co-stationarity.ps, co-stationarity.pdf.

(Joint with James Cummings) "The hyper-weak distributive law and a related game in Boolean algebras," To appear in the Annals of Pure and Applied Logic. hyper-weak.dvi, hyper-weak.ps, hyper-weak.pdf.

"More ubiquitous undetermined games and other results on uncountable length games in Boolean algebras," To appear in Note di Matematica, Proceedings of the 2nd Workshop on Selection Principals in Mathematics. unctbl_games.ps, unctbl_games.pdf.

"Co-stationarity of the ground model and new $\omega$-seqences," To appear in the Proc. Amer. Math. Soc. new_omega_seq.dvi, new_omega_seq.ps, new_omega_seq.pdf.

"$\kappa$-stationary subsets of $\mathcal{P}_{\kappa^+}\lambda$, infinitary games, and distributive laws in Boolean algebras," To appear in the Journal of Symbolic Logic. games_kstat.dvi, games_kstat.ps, games_kstat.pdf.

(Joint with Sy-David Friedman) "Internal consistency and co-stationarity of the ground model," (Submitted). iconcostat.dvi, iconcostat.ps, iconcostat.pdf.

(Joint with Sy-David Friedman) "Homogeneous iteration and measure one covering relative to HOD," (Submitted).

(Joint with Karel Prikry) "On perfect trees and distributity," (In progress.)