Assistant Professor
Department of Mathematics and Applied Mathematics
Virginia Commonwealth University

My research is in the field of set theory. Most of my recent work is on ideals associated to large cardinals. For example, I've done work on combinatorial principles and forcing constructions related to the large cardinal properties of indescribability and Ramseyness. I've also worked on strong properties of successor cardinals that hold after collapsing large cardinals and on preserving large cardinals through Easton-support forcing iterations.

We hosted a MAMLS meeting at VCU on April 1 & 2, 2017. Thanks to Arthur Apter and Hugh Woodin for their generous support.

See the VCU Analysis, Logic and Physics Seminar (ALPS) website for upcoming talks.

I got my Ph.D. with Joel D. Hamkins at the CUNY Graduate Center.

Here are some notes from a course in model theory, which I taught jointly with Sean Cox, and which was offered in the spring of 2014 at VCU.


  1. (with Peter Holy) Higher indescribability and ideal operators. (In preparation)
  2. Higher indescribability and derived topologies. (Submitted, 45 pages - [arxiv], [pdf])
  3. Large cardinal ideals. (Accepted chapter for Research Trends in Contemporary Logic, 49 pages - [arxiv], [pdf])
  4. (with Victora Gitman and Chris Lambie-Hanson) Forcing a \(\square(\kappa)\)-like principle to hold at a weakly compact cardinal. (Accepted at Annals of Pure and Applied Logic - [arxiv], [pdf])
  5. A refinement of the Ramsey hierarchy via indescribability. Journal of Symbolic Logic, 85 (2):773-808, 2020. - ([arxiv], [pdf])
  6. Characterizations of the weakly compact ideal on \(P_\kappa\lambda\). Annals of Pure and Applied Logic, 171 (6):23 pages, 2020. ([arxiv], [pdf])
  7. (with Hiroshi Sakai) The weakly compact reflection principle need not imply a high order of weak compactness. Archive for Mathematical Logic, 59 (1):179-196, 2020. ([arxiv], pdf], [journal])
  8. Adding a non-reflecting weakly compact set. Notre Dame Journal of Formal Logic, 60 (3):503-521, 2019. ([arxiv], [pdf], [journal])
  9. (with Monroe Eskew) Rigid ideals, Israel Journal of Mathematics, 224 (1):343-366, 2018 ([arxiv], [pdf], [journal])
  10. (with Sean Cox) Indestructibility of generically strong cardinals, Fundamenta Mathematicae, 232 (2):131-149, 2016 ([arxiv], [pdf] or [journal])
  11. (with Moti Gitik, Joel David Hamkins, and Jason Schanker) The least weakly compact cardinal can be unfoldable, weakly measurable and nearly \(\theta\)-supercompact, Archive for Mathematical Logic, 54 (5-6):491-510, 2015 ([arxiv], [pdf] or [journal])
  12. (with Victoria Gitman) Easton's theorem for Ramsey and strongly Ramsey cardinals, Annals of Pure and Applied Logic, 166 (9):934-952, 2015. ([arxiv], [pdf] or [journal])
  13. (with Sy Friedman and Radek Honzik) Easton functions and supercompactness, Fundamenta Mathematicae, 226 (3):279-296, 2014. ([arxiv], [pdf] or [journal])
  14. (with Menachem Magidor) On Supercompactness and the continuum function, Annals of Pure and Applied Logic, 165 (2):620-630, 2014. ([arxiv], [pdf] or [journal])
  15. Easton's Theorem in the presence of Woodin cardinals, Archive for Mathematical Logic, 52 (5-6):569-591, 2013. ([arxiv], [pdf] or [journal])
  16. (with A. W. Apter) Consecutive singular cardinals and the continuum function, Notre Dame Journal of Formal Logic, 54 (2):125-136, 2013. ([arxiv], [pdf] or [journal])
  17. The failure of GCH at a degree of supercompactness, Mathematical Logic Quarterly, 58 (1-2):83-94, 2012. ([arxiv], [pdf] or [journal])


Spring 2021
Fall 2020
Spring 2020
Fall 2019
Spring 2019
Fall 2018
Spring 2018
Fall 2017
Spring 2017
Fall 2016
Spring 2016
Fall 2015
Spring 2015
Fall 2014
Spring 2014
Fall 2013