Research
In this section you can find a list of my research topics. Clicking on a topic will toggle the list of my papers on that topic; clicking on the title of a paper will toggle downloading options. Publications that belong to the intersection of two or more topics will appear multiple times (one under each heading).
Combinatorics/Combinatorial Set Theory Consistency and Independence Proofs
(with Jareb Navarro-Castillo and Jesús A. Soria-Rojas): Q-points, selective ultrafilters, and idempotents, with an application to choiceless set theory Hindman's Theorem in the hierarchy of Choice Principles. Journal of Mathematical Logic 24 no. 1 (2024), 2350002.
(With Joshua Brot and Mengyang Cao): Finiteness classes arising from Ramsey-theoretic statements in set theory without choice. 172 no. 6 (2021), 102961.
Stable ordered union ultrafilters and $\mathrm{cov}(\mathcal{M})<\mathfrak c$ 84 no. 3 (2019), 1176-1193.
(With Michael Hrušák ): A parametrized diamond principle and union ultrafilters. 153 no. 2 (2018), 261-271.
(With Michael Hrušák ): Gruff ultrafilters. 210 (2016), 355-365; as well as a corrigendum to this paper (Topology Appl. 231 (2017), 430-431).
Strongly Summable Ultrafilters: Some properties and Generalizations. Strongly Summable Ultrafilters, Union Ultrafilters, and the Trivial Sums Property. 68 (2016), 44-66.
Set Theory without the Axiom of Choice Computability Theory, Reverse Mathematics Algebra in the Čech-Stone compactification
(with Jareb Navarro-Castillo and Jesús A. Soria-Rojas): Q-points, selective ultrafilters, and idempotents, with an application to choiceless set theory Using ultrafilters to prove Ramsey-type theorems. 129 no. 2 (2022), 116-131.
Stable ordered union ultrafilters and $\mathrm{cov}(\mathcal{M})<\mathfrak c$ 84 no. 3 (2019), 1176-1193.
(With Michael Hrušák ): A parametrized diamond principle and union ultrafilters. 153 no. 2 (2018), 261-271.
(With Martino Lupini ): Strongly productive ultrafilters on semigroups. 92 (2016), 242-257.
Strongly Summable Ultrafilters: Some properties and Generalizations. Strongly Summable Ultrafilters, Union Ultrafilters, and the Trivial Sums Property. 68 (2016), 44-66.
Every strongly summable ultrafilter on $\bigoplus\mathbb Z_2$ is sparse. 19
(2013), 117-129.
Topology (General or Otherwise), Dynamical Systems Powered by
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