Research

I am no longer active in producing research, though I still referee papers.

My research interests were in mathematical logic, specializing in set theory. Much of my set theoretic work was motivated by the multiversist view of Hamkins and others. There are many different universes of set theory. What are the possibilities? What is the structure of the set theoretic multiverse? For instance, I have work in set theoretic geology, in models of set theory, including nonstandard models, and in the foundations of forcing.

Outside of pure set theory, I was interested in set theory’s connections to other areas of logic and to philosophy of mathematics. My work touched upon model theory, computability theory, the study of modal logics, and the philosophy of set theory.

My Publications

• Alfredo Roque Freire and Kameryn J. Williams, Non-tightness in class theory and second-order arithmetic, The Journal of Symbolic Logic (to appear).

• Neil Barton and Kameryn J. Williams, Varieties of class-theoretic potentialism, The Review of Symbolic Logic (to appear).

• Joel David Hamkins and Kameryn J. Williams, The Sigma_1-definable universal finite sequence, The Journal of Symbolic Logic (2020).

• Victoria Gitman, Joel David Hamkins, Peter Holy, Philipp Schlicht, and Kameryn Williams, The exact strength of the class forcing theorem, The Journal of Symbolic Logic (2020).

• Jonas Reitz and Kameryn J. Williams, Inner mantles and iterated HOD, Mathematical Logic Quarterly (2019).

• Kameryn J. Williams, Minimum models of second-order set theories, Journal of Symbolic Logic (2019).

• Miha E. Habič, Joel David Hamkins, Lukas Daniel Klausner, Jonathan Verner, and Kameryn J. Williams, Set-theoretic blockchains, Archive for Mathematical Logic (2019).

• Joel David Hamkins, Russell Miller, and Kameryn J. Williams, Forcing as a computational process, preprint available.

• Kameryn J. Williams, The omega-th inner mantle, preprint available.

• Kameryn J. Williams, The Structure of Models of Second-order Set Theories, PhD Dissertation, The Graduate Center, CUNY (2018).

Selected Talks

(See here for a list of all talks.)

• How hard is it to compute a failure of the continuum hypothesis, invited talk, Logic Across Mathematics, 2025 AWM Research Symposium (May 2025).

• Solid, neat, tight: toward charting the boundary of definability, invited talk, NERDS 25.0 (Nov 2024).

• Mediacy and independence, invited talk, 120 Years of Choice (Jul 2024).

• Mediate cardinals, CUNY Logic Workshop (Mar 2024).

• Nonstandard methods versus Nash-Willaims, invited talk, MAMLS Spring Fling 2023 (May 2023).

• Non-tightness in class theory, contributed talk, ASL North America Annual Meeting 2023 (Mar 2023).

• Tightness in second-order arithmetic, CUNY MOPA Seminar (Oct 2022).

• The potentialist multiverse of classes, Leeds Models and Sets Seminar (Mar 2022).

• Potentialism about sets, potentialism about classes, invited talk, Early Career Researcher Workshop 2021 (Oct 2021).

• Incompleteness and the universal algorithm, Hofstra Mathematics Seminar (Apr 2021).

• The geology of inner mantles, Oxford Set Theory Seminar (Dec 2020).

• The universal algorithm and arithmetic potentialism, Analysis, Logic, and Physics Seminar, VCU (Oct 2020).

• On axioms for multiverses of set theory, contributed talk, RIMS Set Theory Workshop 2019 (Nov 2019).

• The Sigma_1 universal finite sequence, contributed talk, 7th biannual European Set Theory Conference (July 2019).

• Inner mantles and iterated HOD, contributed talk, 2019 ASL North American Annual Meeting (May 2019).

• Amalgamating generic reals, a surgical approach, Logic Seminar, UH Mānoa (Jan 2019).

• The universal Sigma_1 finite sequence, contributed talk, Cantor Meets Robinson conference (Dec 2018).

• Minimal models for second-order set theories, contributed talk, 2018 ASL North American Annual Meeting (May 2018).

• On the length of iterated full satisfaction classes, Warsaw Workshop on Formal Truth Theories (Sept 2017).

• The exact strength of the class forcing theorem, Research Seminar, Kurt Gödel Research Center (Sept 2017).

• Admissible covers and compactness arguments for ill-founded models of set theory, Set Theory Seminar, CUNY (Sept 2015).

• A perfectly generic talk, MoPA Seminar, CUNY (Apr 2015).

• Scott’s problem for models of set theory, oral exam, in Set Theory Seminar, CUNY (Oct 2014).