writings
A collection of publications, expository writings, and talks given
Publications
- (Preprint) Discrete Generators on Pseudotrees (pdf)
Description: We characterize when tree-like pseudotrees admit a (0,1)-generator such that that every member of the generator is {0,1}-valued.
Journal: Topology Proceedings
Submitted: 6/19/2026
Accepted: 8/10/2026
Expository papers
- Diamond Equivalents (pdf)
Description: We state and prove 4 other equivalent formuations of the diamond principle. - Functional countability of the square of the Kunen line minus the diagonal (pdf)
Description: We give a brief overview of functional coutnability, the Kunen line construction, and a possible answer to a question posed paper by V. Tkachuk. - Boolean algebras of arbitrary size (pdf)
Description: We state and prove a well known result from Solovay about the existence of countably generated complete Boolean algebras of size larger than an arbitrary cardinality. - Super (0,1)-generators on trees of arbitrary size (pdf)
Description: (0,1)-generators of Tychonoff spaces capture the topology of the space inside of Cp(X) space. Trees of arbitrary height with the restriction that every element has at most countably many successors is shown to have a super (0,1)-generator that is also discrete.
Talks given
- An Introduction to Forcing (slides)
UofSC Math Grad Colloquium - 3/16/2022 - Countably Generated Complete Boolean Algebras of Arbitrary Size (slides)
UofSC Math Grad Colloquium - 9/21/2021 - Monotoncity of Quantum Entropy (slides)
UofSC Math Grad Colloquium - 4/30/2025 - Discrete Generators on Pseudotrees (slides)
UofSC Math Grad Colloquium - 9/16/2026