# Publications

# 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*.