# Publications

# Publications and other writing

On splitting and splittable families

With Bryce Frederickson, Samuel Mathers, and Hao-Tong Yan.

Conjugacy for homogeneous ordered graphs

With Paul Ellis. *Archive for mathematical logic*, 2019. (ordered graphs in journal)

Hyperbinary numbers and fraction trees

With Paul Ellis and Japheth Wood. *MTC Magazine*, 2018.

On the classification of automorphisms of trees

With Kyle Beserra. Accepted to *Contributions to discrete mathematics*.

The classification of countable models of set theory

With John Clemens and Samuel Dworetzky.

On the classification of vertex-transitive structures

With John Clemens and Stephanie Potter. *Archive for mathematical logic*, 2019. (vertex-transitive structures in journal)

The set splittability problem

With P. Bernstein, C. Bortner, S. Li, and C. Simpson.

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. (elliott review in journal)

The conjugacy problem for automorphism groups of homogeneous digraphs

With Paul Ellis. *Contributions to discrete mathematics*, 2017. (homogeneous digraphs in journal)

On generalizations of separating and splitting families

With Daniel Condon, Luke Serafin, and Cody Stockdale. *Electronic journal of combinatorics*, 2016. (separating families in 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.

The conjugacy problem for automorphism groups of countable homogeneous structures

With Paul Ellis. *Mathematical logic quarterly*, 2016. (homogeneous structures in journal)

A López-Escobar theorem for metric structures, and the topological Vaught conjecture

With Martino Lupini. *Fundamenta mathematicae*, 2016. (lopez-escobar in journal)

Ioana’s superrigidity theorem and orbit equivalence relations

*ISRN algebra*, 2013. (superrigidity applications in journal)

Generalized Choquet spaces

With Philipp Schlicht. *Fundamenta mathematicae*, 2016. (choquet spaces in journal)

The fundamental theorem on symmetric polynomials

History’s first whiff of Galois theory. With Ben Blum-Smith. *College mathematics journal*, 2017. (symmetric polynomials in journal)

Borel Tukey morphisms and combinatorial cardinal invariants

With Tamás Mátrai and Juris Steprāns. *Fundamenta mathematicae*, 2013. (tukey morphisms in journal)

Automorphisms of corona algebras, and group cohomology

With Ilijas Farah. *Transactions of the American mathematical society*, 2014. (corona algebras in journal)

The hierarchy of equivalence relations on the natural numbers under computable reducibility

With Joel Hamkins and Russell Miller. *Computability*, 2012. (computable reducibility in journal)

Review of Invariant descriptive set theory

Review of “Invariant descriptive set theory” by Su Gao. *Bulletin of symbolic logic*, 2011. (gao review in journal)

Cardinal characteristics and countable Borel equivalence relations

With Scott Schneider. *Mathematical logic quarterly*, 2017. (cardinal characteristics in 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. (ittm applications in journal)

Infinite time decidable equivalence relation theory

With Joel Hamkins. *Notre Dame journal of formal logic*, 2011. (ittm reducibility in journal)

Borel reductions of profinite actions of SLn(Z)

*Annals of pure and applied logic*, 2010. (profinite actions in journal)

The complexity of classification problems for models of arithmetic

With Roman Kossak. *Bulletin of symbolic logic*, 2010. (peano arithmetic in journal)

The conjugacy problem for the automorphism group of the random graph

With Paul Ellis and Scott Schneider. *Archive for mathematical logic*, 2011. (random graph in 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. (abelian groups in journal)

Descriptive aspects of torsion-free abelian groups

Doctoral thesis, Rutgers University, 2008. (descriptive aspects in repository)