Academic History

Bard College at Simon’s Rock

Assist Professor of Mathematics, Division of Science, Computing, and Mathematics

Fall 2023 to Spring 2025

Sam Houston State University

Visiting Assistant Professor, Department of Mathematics and Statistics

Fall 2021 to Spring 2023

University of Hawaiʻi at Mānoa

Temporary Assistant Professor, Department of Mathematics

Fall 2018 to Spring 2021

Education

Ph.D. in Mathematics May 2018

The Graduate Center, The City University of New York

Dissertation Advisor: Joel David Hamkins

Dissertation: The Structure of Models of Second-order Set Theories

B.S. in Mathematics, Dec 2012

Boise State University (High Honors)

Minor in Computer Science

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)

Teaching and Educational Experience

• (2023–2025) Bard College at Simon’s Rock. Assistant Professor.

• (2021–2023) Sam Houston State University. Visiting Assistant Professor.

• (2018–2021) University of Hawaiʻi at Mānoa. Temporary Assistant Professor.

• (2017–2018) Bronx Community College, CUNY. Quantitative reasoning fellow.

• (2013–2017) Brooklyn College, CUNY. Graduate teaching fellow.

Conference 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).

• Solid, neat, tight: toward charting the boundary of definability, invited talk, NERDS 25.0 (Meeting canceled due to weather) (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).

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

• Coding sets into inner mantles, contributed talk, BEST 2021 (June 2021).

• 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).

• 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).

• Minimal models of Kelley–Morse set theory, Boise Extravaganza in Set Theory, AAAS Pacific Division 97th annual meeting (June 2016).

• Minimal models of second-order set theories, New York Graduate Student Logic Conference (May 2016).

• Minimal models of second-order set theories, Set Theory Day, The Graduate Center, CUNY (March 2016).

Seminar Talks

• Is forcing a computable procedure?, Connecticut Logic Seminar (Nov 2024).

• Infinity, the axiom of choice, and mediacy, Simon’s Rock Mathematics Colloquium (Sept 2024).

• Mediate cardinals, CUNY Set Theory Seminar (Apr 2024).

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

• A nonstandard approach to integer combinatorics, Boise State TATERS (Nov 2023).

• Interpretations and bi-interpretations in second-order arithmetic, Online Logic Seminar (Oct 2023).

• The universal algorithm, the universal finite sequence, and potentialism, SHSU Colloquium (Feb 2023).

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

• Inner mantles: good, bad, and ugly, Barcelona Set Theory Seminar (June 2022).

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

• Potentialism about classes, CUNY Set Theory Seminar (Oct 2021).

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

• Varieties of class theoretic potentialism, Konstanz Philosophy of Math Seminar (Dec 2020).

• 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).

• Incompleteness, the universal algorithm, and arithmetic potentialism, TMWYF Seminar (Sept 2020).

• End-extensions of models of set theory and the Sigma_1 universal finite sequence, Virtual MOPA Seminar, CUNY (July 2020).

• The geology of inner mantles, Virtual Set Theory Seminar, CUNY (May 2020).

• The computable structure theory of forcing, Seminari de lògica de Barcelona, Universitat de Barcelona (May 2019).

• Transfinite Recursion from Gödel–Bernays to Kelley–Morse, Set Theory Seminar, CUNY (May 2019).

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

• The Universal Algorithm, the Universal Sigma_1 Finite Sequence, and Set-theoretic Potentialism, Department Colloquium, UH Mānoa (Nov 2018).

• Forcing as a computational process, Logic Seminar, UH Mānoa (Sept 2018).

• A conceptual overview of forcing, Logic Seminar, UH Mānoa (Sept 2018).

• Universes of sets, Logic Seminar, UH Mānoa (Aug 2018).

• The structure of models of second-order set theories, dissertation defense, in Set Theory Seminar, CUNY (Apr 2018).

• Forcing over arithmetic: a second-order approach, MoPA Seminar, CUNY (Feb 2018).

• Beta models of ATR_0, MoPA Seminar, CUNY (Nov 2018).

• Strong second-order set theories do not have least transitive models, Logic and Computation Seminar, University of Pennsylvania (Nov 2017).

• The exact strength of the class forcing theorem, Set Theory Seminar, CUNY (Oct 2017).

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

• Non-hyperfinite countable equivalence relations, MoPA Seminar, CUNY (Mar 2017).

• Separating class determinacy, Set Theory Seminar, CUNY (Nov 2016).

• Models of arithmetic with two expansions to a model of ACA_0, MoPA Seminar, CUNY (Oct 2016).

• Yet more forcing in arithmetic: life in a second-order world, MoPA Seminar, CUNY (Sept 2016).

• Recursive definability of the standard cut, MoPA Seminar, CUNY (Oct 2015).

• Is there a least transitive model of Kelley–Morse set theory?, Set Theory Seminar, CUNY (Oct 2015).

• 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).

• Rather classless models of set theory and second-order set theory, Set Theory Seminar, CUNY (Mar 2015).

• Forcing over models of arithmetic, MoPA Seminar, CUNY (Nov 2014).

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

• On the independence of the Borel conjecture, Set Theory Seminar, CUNY (Apr 2014).