Research

Papers

• Descending sequences in reflection hierarchies, with Mateusz Łełyk

• Ranking theories via encoded β-models, with Hanul Jeon, Patrick Lutz, Fedor Pakhomov

• A classification of incompleteness statements, with Henry Towsner [arXiv]

• Modal definability in Kripke's theory of truth [arXiv]

• Generalized ordinal analysis and reflection principles in set theory, with Hanul Jeon [arXiv]

• A theory satisfying a strong version of Tennenbaum's theorem, with Patrick Lutz [arXiv]

• Reflection ranks via infinitary derivations [arXiv]

• On the hierarchy of natural theories [arXiv]

• An incompleteness theorem via ordinal analysis
  The Journal of Symbolic Logic, 18(1), 80--96, 2024 [published version | arXiv]

• Reducing ω-model reflection to iterated syntactic reflection, with Fedor Pakhomov
  Journal of Mathematical Logic, 23(2):1--39, 2023 [published version | corrigendum | arXiv]

• Characterizations of ordinal analysis
  Annals of Pure and Applied Logic, 174(4), 2023 [published version | arXiv]

• Evitable iterates of the consistency operator
  Computability, 12(1):59--69, 2023 [published version | arXiv]

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

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

• 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 2013 ACM International Symposium on New Ideas, New Paradigms, and Reflections on Programming & Software:1--16, 2013 [published version]

Recorded Talks

• Is the consistency operator canonical?
  UConn Logic Colloquium, 3/22/24 [link]

• New results on incompleteness and ordinal analysis
  Lectures on Logic and Foundations of Mathematics, 11/8/23 [link]

• An incompleteness theorem via ordinal analysis
  Steklov Institute Logic Online Seminar, 10/25/21 [link]

• On the hierarchy of natural theories
  International Workshop on Gödel's Incompleteness Theorems, 8/18/21 [link]

• Reducing ω-model reflection to iterated syntactic reflection
  CUNY Models of Peano Arithmetic Seminar, 2/2/21 [link]

• On the naturalness of the consistency operator
  Workshop on Proof Theory, Modal Logic, and Reflection Principles, 10/17/17 [link]

Dissertation

• Reflection principles and ordinal analysis
  University of California, Berkeley, Group in Logic, 2020 [escholarship]