Publications and other writing

New jump operators on equivalence relations
With John Clemens.

 

Computable reducibility of equivalence relations and an effective jump operator
With John Clemens and Gianni Krakoff.

 

On splitting and splittable families
With Bryce Frederickson, Samuel Mathers, and Hao-Tong Yan.

2021

Category, measure, and forcing: Set theory lecture notes
With Erik Holmes. Open Math Notes, American mathematical society.

2020

The classification of countable models of set theory
With John Clemens and Samuel Dworetzky. Mathematical logic quarterly 66(2):182-189.

 

Trends in set theory
Editor, with Grigor Sargsyan. Simon Fest conference in honor of Simon Thomas’s 60th birthday. Contemporary mathematics 752, American mathematical society.

2019

On the classification of automorphisms of trees
With Kyle Beserra. Contributions to discrete mathematics 14(1):203–213.

 

The set splittability problem
With P. Bernstein, C. Bortner, S. Li, and C. Simpson. Australasian journal of combinatorics 75(2):190–209.

 

On the classification of vertex-transitive structures
With John Clemens and Stephanie Potter. Archive for mathematical logic 58(5–6):565–574.

 

Conjugacy for homogeneous ordered graphs
With Paul Ellis. Archive for mathematical logic 58(3–4):457–467.

2018

Hyperbinary numbers and fraction trees
Educational article with Paul Ellis and Japheth Wood. MTC Magazine, Spring issue.

2017

The fundamental theorem on symmetric polynomials: history’s first whiff of Galois theory
With Ben Blum-Smith. College mathematics journal 48(1):18–29.

 

Cardinal characteristics and countable Borel equivalence relations
With Scott Schneider. Mathematical logic quarterly 63(3–4):211–227.

 

The conjugacy problem for automorphism groups of homogeneous digraphs
With Paul Ellis. Contributions to discrete mathematics 12(1):62–73.

2016

The conjugacy problem for automorphism groups of countable homogeneous structures
With Paul Ellis. Mathematical logic quarterly 62(6):580–589.

 

On generalizations of separating and splitting families
With Daniel Condon, Luke Serafin, and Cody Stockdale. Electronic journal of combinatorics 23(3):P3.36.

 

Generalized Choquet spaces
With Philipp Schlicht. Fundamenta mathematicae 232:227–248.

 

A López-Escobar theorem for metric structures, and the topological Vaught conjecture
With Martino Lupini. Fundamenta mathematicae 234:55–72.

2015

Two articles on the classification of C* algebras
Review of “The isomorphism relation for separable C* algebras” by G. Elliott, I. Farah, et al, and “Completeness of the isomorphism problem for separable C* algebras” by M. Sabok. Bulletin of symbolic logic 21(4):427–430.

2014

The classification problem for finitely generated operator systems and spaces
Research report with M. Argerami, M. Kalantar, M. Kennedy, M. Lupini, and M. Sabok.

 

Automorphisms of corona algebras, and group cohomology
With Ilijas Farah. Transactions of the American mathematical society 366:3611–3630.

2013

Infinite time Turing machines and an application to the hierarchy of equivalence relations on the reals
Expository article with Joel Hamkins. Appears in “Effective mathematics of the uncountable”, Lecture notes in logic 41:33-49.

 

Ioana’s superrigidity theorem and orbit equivalence relations
Expository article appears in ISRN algebra.

 

Borel Tukey morphisms and combinatorial cardinal invariants
With Tamás Mátrai and Juris Steprāns. Fundamenta mathematicae 223:29–48.

2012

The classification of torsion-free abelian groups of finite rank up to isomorphism and up to quasi-isomorphism
Transactions of the American mathematical society 364:175–194.

 

The hierarchy of equivalence relations on the natural numbers under computable reducibility
With Joel Hamkins and Russell Miller. Computability 1(1):15–38.

2011

Review of Invariant descriptive set theory
Review of “Invariant descriptive set theory” by Su Gao. Bulletin of symbolic logic 17(2):265–267.

 

Infinite time decidable equivalence relation theory
With Joel Hamkins. Notre Dame journal of formal logic 52(2):203–228.

 

The conjugacy problem for the automorphism group of the random graph
With Paul Ellis and Scott Schneider. Archive for mathematical logic 50(1):215–221.

2010

The complexity of classification problems for models of arithmetic
With Roman Kossak. Bulletin of symbolic logic 16(3):345–358.

 

Borel reductions of profinite actions of SLn(Z)
Annals of pure and applied logic 161:1270–1279.

2008

Descriptive aspects of torsion-free abelian groups
Doctoral thesis. Rutgers University Community Repository.