Research

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

Submitted

• Characterizations of ordinal analysis [arXiv]

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

• On the hierarchy of natural theories [arXiv]

• Use and mention in formal languages

Published

Journal Articles

• An incompleteness theorem via ordinal analysis
  The Journal of Symbolic Logic, online, 1--17, 2022 [published version | arXiv]

• Evitable iterates of the consistency operator
  Computability: The Journal of the Association CiE, online, 1--11, 2022 [published version | arXiv]

• 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]

Conference Proceedings

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

Reviews

• A note on the unprovability of consistency in formal theories of truth, by Kevin Davey
  Mathematical Reviews, MR4340960, 2022

• A dialogical route to logical pluralism, by Rohan French
  Mathematical Reviews, MR4306106, 2022

• Local reflection, definable elements, and 1-provability, by Evgeny Kolmakov
  Mathematical Reviews, MR4159764, 2022