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Brent Cody

Brent Cody

Associate Professor, Department of Mathematics and Applied Mathematics

Virginia Commonwealth University

Email: bmcody@vcu.edu

Research Overview

My primary area of research is set theory and involves large cardinals. I've done work on combinatorial principles and forcing constructions related to the large cardinal properties of Ramseyness, ineffability and indescribability.

I also work on problems in graph theory, that grew out of an interest in connections between mathematics and music theory via maximally even sets and Euclidean rhythms (see [20] and [21] below).

Papers

  1. The k-general d-position problem for graphs. (with Garrett Moore) Discrete Applied Mathematics 366: 135–151, 2025. (pdf)
  2. Large cardinal ideals. Accepted chapter for Research Trends in Contemporary Logic, 49 pages. (pdf)
  3. Sets of vertices with extremal energy. (with Neal Bushaw and Chris Leffler) Accepted at Discrete Mathematics. (pdf)
  4. The Music and Mathematics of Maximally Even Sets. (with Neal Bushaw, Luke Freeman and Tobias Whitaker) Proceedings of Bridges 2024: Mathematics, Art, Music, Architecture, Culture: pp. 61-68. (pdf)
  5. Two-cardinal derived topologies, indescribability and Ramseyness. (with Chris Lambie-Hanson and Jing Zhang) Accepted at Journal of Symbolic Logic. (pdf)
  6. Two-cardinal ideal operators and indescribability. (with Philip White) Annals of Pure and Applied Logic, 175 (8): Paper No. 103463, 17 pp., 2024. (pdf)
  7. Higher indescribability and derived topologies. Journal of Mathematical Logic 24 (1): Paper No. 2350001, 48 pp., 2024. (pdf)
  8. Sparse analytic systems. (with Sean Cox and Kayla Lee) Forum of Mathematics, Sigma, Paper No. e58, 9 pp., 2023. (pdf)
  9. Ideal operators and higher indescribability. (with Peter Holy) Journal of Symbolic Logic, 88 (2):835-873, 2023. (pdf)
  10. Forcing a ◻(κ)-like principle to hold at a weakly compact cardinal. (with Victoria Gitman and Chris Lambie-Hanson) Annals of Pure and Applied Logic, 172 (7):102960, 26 pp., 2021. (pdf)
  11. A refinement of the Ramsey hierarchy via indescribability. Journal of Symbolic Logic, 85 (2):773-808, 2020. (pdf)
  12. Characterizations of the weakly compact ideal on Pκλ. Annals of Pure and Applied Logic, 171 (6):23 pages, 2020. (pdf)
  13. The weakly compact reflection principle need not imply a high order of weak compactness. (with Hiroshi Sakai) Archive for Mathematical Logic, 59 (1):179-196, 2020. (pdf)
  14. Adding a non-reflecting weakly compact set. Notre Dame Journal of Formal Logic, 60 (3):503-521, 2019. (pdf)
  15. Rigid ideals. (with Monroe Eskew) Israel Journal of Mathematics, 224 (1):343-366, 2018. (pdf)
  16. Indestructibility of generically strong cardinals. (with Sean Cox) Fundamenta Mathematicae, 232 (2):131-149, 2016. (pdf)
  17. The least weakly compact cardinal can be unfoldable, weakly measurable and nearly θ-supercompact. (with Moti Gitik, Joel David Hamkins, and Jason Schanker) Archive for Mathematical Logic, 54 (5-6):491-510, 2015. (pdf)
  18. Easton's theorem for Ramsey and strongly Ramsey cardinals. (with Victoria Gitman) Annals of Pure and Applied Logic, 166 (9):934-952, 2015. (pdf)
  19. Easton functions and supercompactness. (with Sy Friedman and Radek Honzik) Fundamenta Mathematicae, 226 (3):279-296, 2014. (pdf)
  20. On Supercompactness and the continuum function. (with Menachem Magidor) Annals of Pure and Applied Logic, 165 (2):620-630, 2014. (pdf)
  21. Easton's Theorem in the presence of Woodin cardinals, Archive for Mathematical Logic, 52 (5-6):569-591, 2013. (pdf)
  22. Consecutive singular cardinals and the continuum function. (with A. W. Apter) Notre Dame Journal of Formal Logic, 54 (2):125-136, 2013. (pdf)
  23. The failure of GCH at a degree of supercompactness. Mathematical Logic Quarterly, 58 (1-2):83-94, 2012. (pdf)

Students

I've worked on many research projects with both undergraduate and graduate students. Names and references to the above publications are listed below.

Undergraduates:
Graduate students:
Master's Theses:

Teaching