# Publications and other writing

Conjugacy for homogeneous ordered graphs
With Paul Ellis. (arχiv | journal)

Hyperbinary numbers and fraction trees
With Paul Ellis and Japheth Wood. (article)

On the classification of automorphisms of trees
With Kyle Beserra. Accepted to Contributions to discrete mathematics. (arχiv)

The classification of countable models of set theory
With John Clemens and Samuel Dworetzky. (arχiv)

On the classification of vertex-transitive structures
With John Clemens and Stephanie Potter. Archive for mathematical logic, 2018. (arχiv | journal)

The set splittability problem
With P. Bernstein, C. Bortner, S. Li, and C. Simpson. (arχiv)

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, 2015. (preprint | journal)

The conjugacy problem for automorphism groups of homogeneous digraphs
With Paul Ellis. Contributions to discrete mathematics, 2017. (arχiv | journal)

On generalizations of separating and splitting families
With Daniel Condon, Luke Serafin, and Cody Stockdale. Electronic journal of combinatorics, 2016. (arχiv | journal)

The classification problem for finitely generated operator systems and spaces
With M. Argerami, M. Kalantar, M. Kennedy, M. Lupini, and M. Sabok. Research report, 2014. (arχiv)

The conjugacy problem for automorphism groups of countable homogeneous structures
With Paul Ellis. Mathematical logic quarterly, 2016. (arχiv | journal)

A López-Escobar theorem for metric structures, and the topological Vaught conjecture
With Martino Lupini. Fundamenta mathematicae, 2016. (arχiv | journal)

Ioana’s superrigidity theorem and orbit equivalence relations
ISRN algebra, 2013. (arχiv | journal)

Generalized Choquet spaces
With Philipp Schlicht. Fundamenta mathematicae, 2016. (arχiv | journal)

The fundamental theorem on symmetric polynomials
History’s first whiff of Galois theory. With Ben Blum-Smith. College mathematics journal, 2017. (arχiv | journal)

Borel Tukey morphisms and combinatorial cardinal invariants
With Tamás Mátrai and Juris Steprāns. Fundamenta mathematicae, 2013. (arχiv | journal)

Automorphisms of corona algebras, and group cohomology
With Ilijas Farah. Transactions of the American mathematical society, 2014. (arχiv | journal)

The hierarchy of equivalence relations on the natural numbers under computable reducibility
With Joel Hamkins and Russell Miller. Computability, 2012. (arχiv | journal)

Review of Invariant descriptive set theory
Review of “Invariant descriptive set theory” by Su Gao. Bulletin of symbolic logic, 2011. (preprint | journal)

Cardinal characteristics and countable Borel equivalence relations
With Scott Schneider. Mathematical logic quarterly, 2017. (arχiv | journal)

Infinite time Turing machines and an application to the hierarchy of equivalence relations on the reals
With Joel Hamkins. Appears in Effective mathematics of the uncountable, ASL Lecture Notes in Logic, 2014. (arχiv | journal)

Infinite time decidable equivalence relation theory
With Joel Hamkins. Notre Dame journal of formal logic, 2011. (arχiv | journal)

Borel reductions of profinite actions of SLn(Z)
Annals of pure and applied logic, 2010. (arχiv | journal)

The complexity of classification problems for models of arithmetic
With Roman Kossak. Bulletin of symbolic logic, 2010. (arχiv | journal)

The conjugacy problem for the automorphism group of the random graph
With Paul Ellis and Scott Schneider. Archive for mathematical logic, 2011. (arχiv | journal)

The classification of torsion-free abelian groups of finite rank up to isomorphism and up to quasi-isomorphism
Transactions of the American mathematical society, 2012. (arχiv | journal)

Descriptive aspects of torsion-free abelian groups
Doctoral thesis, Rutgers University, 2008. (revision | original)