Assistant Professor

Department of Mathematics and Applied Mathematics

Virginia Commonwealth University

bmcody@vcu.edu

My research is in the field of set theory. Most of my recent work is on ideals associated to large cardinals. For example, I've done work on combinatorial principles and forcing constructions related to the large cardinal properties of indescribability and Ramseyness. I've also worked on strong properties of successor cardinals that hold after collapsing large cardinals and on preserving large cardinals through Easton-support forcing iterations.

We hosted a MAMLS meeting at VCU on April 1 & 2, 2017. Thanks to Arthur Apter and Hugh Woodin for their generous support.

See the VCU Analysis, Logic and Physics Seminar (ALPS) website for upcoming talks.

I got my Ph.D. with Joel D. Hamkins at the CUNY Graduate Center.

Here are some notes from a course in model theory, which I taught jointly with Sean Cox, and which was offered in the spring of 2014 at VCU.

PUBLICATIONS

- (with Peter Holy) Higher indescribability and ideal operators. (
*In preparation*) - Higher indescribability and derived topologies. (
*Submitted, 45 pages*- [arxiv], [pdf]) - Large cardinal ideals. (
*Accepted chapter for Research Trends in Contemporary Logic, 49 pages*- [arxiv], [pdf]) - (with Victora Gitman and Chris Lambie-Hanson) Forcing a \(\square(\kappa)\)-like principle to hold at a weakly compact cardinal. (
*Accepted at Annals of Pure and Applied Logic*- [arxiv], [pdf]) - A refinement of the Ramsey hierarchy via indescribability.
*Journal of Symbolic Logic*, 85 (2):773-808, 2020. - ([arxiv], [pdf]) - Characterizations of the weakly compact ideal on \(P_\kappa\lambda\).
*Annals of Pure and Applied Logic*, 171 (6):23 pages, 2020. ([arxiv], [pdf]) - (with Hiroshi Sakai) The weakly compact reflection principle need not imply a high order of weak compactness.
*Archive for Mathematical Logic*, 59 (1):179-196, 2020. ([arxiv], pdf], [journal]) - Adding a non-reflecting weakly compact set.
*Notre Dame Journal of Formal Logic*, 60 (3):503-521, 2019. ([arxiv], [pdf], [journal]) - (with Monroe Eskew) Rigid ideals,
*Israel Journal of Mathematics*, 224 (1):343-366, 2018 ([arxiv], [pdf], [journal]) - (with Sean Cox) Indestructibility of generically strong cardinals,
*Fundamenta Mathematicae*, 232 (2):131-149, 2016 ([arxiv], [pdf] or [journal]) - (with Moti Gitik, Joel David Hamkins, and Jason Schanker) The least weakly compact cardinal can be unfoldable, weakly measurable and nearly \(\theta\)-supercompact,
*Archive for Mathematical Logic*, 54 (5-6):491-510, 2015 ([arxiv], [pdf] or [journal]) - (with Victoria Gitman) Easton's theorem for Ramsey and strongly Ramsey cardinals,
*Annals of Pure and Applied Logic*, 166 (9):934-952, 2015. ([arxiv], [pdf] or [journal]) - (with Sy Friedman and Radek Honzik) Easton functions and supercompactness,
*Fundamenta Mathematicae*, 226 (3):279-296, 2014. ([arxiv], [pdf] or [journal]) - (with Menachem Magidor) On Supercompactness and the continuum function,
*Annals of Pure and Applied Logic*, 165 (2):620-630, 2014. ([arxiv], [pdf] or [journal]) - Easton's Theorem in the presence of Woodin cardinals,
*Archive for Mathematical Logic*, 52 (5-6):569-591, 2013. ([arxiv], [pdf] or [journal]) - (with A. W. Apter) Consecutive singular cardinals and the continuum function,
*Notre Dame Journal of Formal Logic*, 54 (2):125-136, 2013. ([arxiv], [pdf] or [journal]) - The failure of GCH at a degree of supercompactness,
*Mathematical Logic Quarterly*, 58 (1-2):83-94, 2012. ([arxiv], [pdf] or [journal])

TEACHING

Spring 2021

- Math 201 - Calculus with Analytic Geometry I
- Math 490 - Mathematical Expositions

Fall 2020

- Math 201 - Calculus with Analytic Geometry I
- Math 490 - Mathematical Expositions

Spring 2020

- Math 602 - Abstract Algebra II

Fall 2019

- Math 409 - Topology
- Math 502 - Abstract Algebra I

Spring 2019

- Math 301 - Differential Equations
- Math 310 - Linear Algebra

Fall 2018

- Math 697 - Directed Research (Set Theory: Forcing)
- Math 310 - Linear Algebra
- Math 409 - Topology

Spring 2018

- Math 697 - Directed Research (Set Theory: Forcing)
- Math 490 - Mathematical Expositions
- Math 602 - Abstract Algebra II

Fall 2017

- Math 409 - Topology
- Math 490 - Mathematical Expositions

Spring 2017

- Math 591 - Ultrafilters and Applications

Fall 2016

- Math 300 - Introduction to Mathematical Reasoning
- Math 409 - Topology

Spring 2016

- Math 310 - Linear Algebra
- Math 490 - Mathematical Expositions

Fall 2015

- Math 201 - Calculus II
- Math 300 - Intro. to Mathematical Reasoning

Spring 2015

- Math 201 - Calculus II
- Math 490 - Mathematical Expositions
- Math 492 - Independent Study (Computability Theory and Gödel's Incompleteness Theorems)

Fall 2014

- Math 201 - Calculus II
- Math 490 - Mathematical Expositions
- Math 492 - Independent Study (Set Theory)

Spring 2014

- Math 201 - Calculus II
- Math 490 - Mathematical Expositions (taught jointly with Sean Cox)
- Math 591 - Topics Course: Logic and Mathematical Structures (taught jointly with Sean Cox) (notes)
- Math 492 - Independent Study (Set Theory)

Fall 2013

- Math 201 - Calculus II
- Math 300 - Introduction to Mathematical Reasoning