Brent Cody

Brent Cody

Associate Professor, Department of Mathematics and Applied Mathematics

Virginia Commonwealth University

Email: bmcody@vcu.edu

Research Overview

My primary research focus lies within set theory, with particular emphasis on large cardinals. I have explored various aspects of combinatorial principles and developed forcing constructions associated with large cardinal properties, including Ramseyness, ineffability and indescribability. In addition to my work in set theory, I investigate problems in graph theory, which stemmed from an interest in connections between mathematics and music theory, specifically, maximally even sets and Euclidean rhythms, as discussed in [21] and [22] below.

Papers

  1. The Wiener index of vertex colorings. (with Viktoriya Bardenova, Neal Bushaw, Paul Fay and Maya Tennant) Submitted (pdf)
  2. The \(k\)-general \(d\)-position problem for graphs. (with Garrett Moore) Discrete Applied Mathematics, 366: 135–151, 2025. (pdf)
  3. Sets of vertices with extremal energy. (with Neal Bushaw and Chris Leffler) Discrete Mathematics, 348 (7): Paper no. 114466, 2025. (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. Large cardinal ideals. Accepted chapter for Research Trends in Contemporary Logic, 49 pages. (pdf)
  9. Sparse analytic systems. (with Sean Cox and Kayla Lee) Forum of Mathematics, Sigma, Paper No. e58, 9 pp., 2023. (pdf)
  10. Ideal operators and higher indescribability. (with Peter Holy) Journal of Symbolic Logic, 88 (2):835-873, 2023. (pdf)
  11. Forcing a \(\square(\kappa)\)-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)
  12. A refinement of the Ramsey hierarchy via indescribability. Journal of Symbolic Logic, 85 (2):773-808, 2020. (pdf)
  13. Characterizations of the weakly compact ideal on \(P_\kappa\lambda\). Annals of Pure and Applied Logic, 171 (6):23 pages, 2020. (pdf)
  14. 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)
  15. Adding a non-reflecting weakly compact set. Notre Dame Journal of Formal Logic, 60 (3):503-521, 2019. (pdf)
  16. Rigid ideals. (with Monroe Eskew) Israel Journal of Mathematics, 224 (1):343-366, 2018. (pdf)
  17. Indestructibility of generically strong cardinals. (with Sean Cox) Fundamenta Mathematicae, 232 (2):131-149, 2016. (pdf)
  18. The least weakly compact cardinal can be unfoldable, weakly measurable and nearly \(\theta\)-supercompact. (with Moti Gitik, Joel David Hamkins, and Jason Schanker) Archive for Mathematical Logic, 54 (5-6):491-510, 2015. (pdf)
  19. Easton's theorem for Ramsey and strongly Ramsey cardinals. (with Victoria Gitman) Annals of Pure and Applied Logic, 166 (9):934-952, 2015. (pdf)
  20. Easton functions and supercompactness. (with Sy Friedman and Radek Honzik) Fundamenta Mathematicae, 226 (3):279-296, 2014. (pdf)
  21. On Supercompactness and the continuum function. (with Menachem Magidor) Annals of Pure and Applied Logic, 165 (2):620-630, 2014. (pdf)
  22. Easton's Theorem in the presence of Woodin cardinals, Archive for Mathematical Logic, 52 (5-6):569-591, 2013. (pdf)
  23. Consecutive singular cardinals and the continuum function. (with A. W. Apter) Notre Dame Journal of Formal Logic, 54 (2):125-136, 2013. (pdf)
  24. The failure of GCH at a degree of supercompactness. Mathematical Logic Quarterly, 58 (1-2):83-94, 2012. (pdf)

Research With 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