Research

My research is primarily in logic and the foundations of mathematics. My dissertation received the 2020 Sacks Prize from the Association for Symbolic Logic for the most outstanding dissertation in mathematical logic worldwide.

Published

• Reducing ω-model reflection to iterated syntactic reflection, with Fedor Pakhomov
  Journal of Mathematical Logic, online, 1--39, 2021 [published version | arXiv]

• Reflection ranks and ordinal analysis, with Fedor Pakhomov
  The Journal of Symbolic Logic, 86(4):1350--1384, 2021 [published version | arXiv]

• Incompleteness and jump hierarchies, with Patrick Lutz
  Proceedings of the American Mathematical Society, 148(11):4997--5006, 2020 [published version | corrigendum | arXiv]

• A note on the consistency operator
  Proceedings of the American Mathematical Society, 148(6):2645--2654, 2020 [published version | arXiv]

• On the inevitability of the consistency operator, with Antonio Montalbán
  The Journal of Symbolic Logic, 84(1):205--225, 2019 [published version | arXiv]

• Usable security as a static-analysis problem, with Kathi Fisler, Shriram Krishnamurthi, Hannah Quay-de la Vallee, William Zimrin
  Proceedings of the Association for Computing Machinery: International Symposium on New Ideas, New Paradigms, and Reflections on Programming & Software:1--16, 2013 [published version]

Submitted

• Evitable iterates of the consistency operator [arXiv]

• A robust proof-theoretic well-ordering [arXiv]

• A characterization of ordinal analysis [arXiv]

• An incompleteness theorem via ordinal analysis [arXiv]

• Reflection ranks via infinitary derivations, with Fedor Pakhomov [arXiv]

• On the hierarchy of natural theories [arXiv]