# Publications

# Publications and other writing

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. (arχiv)

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 articles: “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. To appear in *Contributions to discrete mathematics*. (arχiv)

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*, 2017. (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 mathematica*, 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 the graduate textbook “Invariant descriptive set theory” by Su Gao. *Bulletin of symbolic logic*, 2011. (preprint | journal)

Cardinal characteristics and countable Borel equivalence relations

With Scott Schneider. Accepted to *Mathematical logic quarterly*, 2016. (arχiv)

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)