Some recent preprints

Unpublished books

The Automorphism Tower Problem

Some preprints

Changing the heights of automorphism towers, with J. Hamkins, accepted for publication in Annals Pure Appl. Logic as of 8/30/99
The automorphism tower problem revisited, with W. Just and S. Shelah, accepted for publication in Advances in Mathematics as of 11/24/98.
On the complexity of the isomorphism relation for finitely generated groups, with B. Velickovic, accepted for publication in J. Algebra as of 11/23/98.
On the complexity of the isomorphism relation for fields of finite transcendence degree, with B. Velickovic, accepted for publication in J. Pure Applied Algebra as of 12/7/99.
Infinite products of finite simple groups II, accepted for publication in Journal of Group Theory as of 10/12/98.
Asymptotic cones of finitely generated groups, with B. Velickovic, accepted for publication in Bull. London Math. Soc as of 3/24/99.
On the complexity of the classification problem for torsion-free abelian groups of rank two, accepted for publication in Acta Mathematica as of 3/30/01.
The classification problem for torsion-free abelian groups of finite rank accepted for publication in J. Amer. Math. Soc. as of 9/14/02.
On the complexity of the classification problem for torsion-free abelian groups of finite rank,
Some applications of superrigidity to Borel equivalence relations, accepted for publication in the Proceedings of the Hajnal Conference as of 4/30/01.
Superrigidity and countable Borel equivalence relations accepted for publication in Annals Pure Appl. Logic as of 5/6/02.
Classifying spaces for proper actions of locally-finite groups, with W. Dicks, P. H. Kropholler and I. J. Leary, accepted for publication in Journal of Group Theory as of 2/12/02.
The virtual isomorphism problem for finitely generated groups accepted for publication in Bull. London Math. Soc. as of 12/3/02
The classification problem for p-local torsion-free abelian groups of finite rank unpublished preprint, April 2002.
Asymptotic cones of finitely presented groups with L. Kramer, S. Shelah and K. Tent, accepted for publication in Advances in Mathematics as of 3/30/04.
Cayley graphs of finitely generated groups accepted for publication in Proc AMS as of 9/1/04.
Property tau and countable Borel equivalence relations accepted for publication in J. Math. Logic as of 3/11/07.
The classification problem for p-local torsion-free abelian groups of rank two with Greg Hjorth, accepted for publication in J. Math. Logic as of 2/23/07.
Borel superrigidity and the classification problem for the torsion-free Abelian groups of finite rank accepted for publication in the Proceedings of the ICM - Madrid, August 22-30, 2006.
Popa superrigidity and countable Borel equivalence relations accepted for publication in Annals Pure Appl. Logic as of 7/31/07.
The classification problem for finite rank Butler groups accepted for publication in Contributions to Module Theory as of 8/10/07.
The commensurability relation for finitely generated groups accepted for publication in Journal of Group Theory as of 12/28/08.
On the complexity of the quasi-isometry and virtual isomorphism problems for finitely generated groups accepted for publication in Groups, Geometry, and Dynamics as of 02/08/08.
A remark on the Higman-Neumann-Neumann Embedding Theorem accepted for publication in Journal of Group Theory as of 9/2/08.
Ultraproducts of finite alternating groups with P. Ellis, S. Hachtman and S. Schneider, to appear in Proceedings of RIMS Workshop on Combinatorial and Descriptive Set Theory.
Martin's Conjecture and Strong Ergodicity accepted for publication in Arch. Math. Logic as of 8/17/09.
Continuous vs. Borel Reductions accepted for publication in Arch. Math. Logic as of 8/3/09.
On the concept of "largeness" in group theory accepted for publication in J. Algebra as of 8/1/09.
On the Number of Universal Sofic Groups accepted for publication in PAMS as of 11/2/2009.
Automorphism groups of ultraproducts of finite symmetric groups, with P. Lücke, accepted for publication in Communications in Algebra as of 6/25/10.
Countable Borel equivalence relations with S. Schneider, to appear in Appalachian Set Theory 2006-2010.
Universal Borel actions of countable groups accepted for publication in Groups, Geometry, and Dynamics.
The Friedman Embedding Theorem accepted for publication in J. Algebra.
A descriptive view of combinatorial group theory accepted for publication in Bull. Symbolic Logic as of 9/15/2010.
The classification problem for S-local torsion-free abelian groups of finite rank accepted for publication in Advances in Mathematics as of 10/19/2010.
On the Steinhaus and Bergman properties for infinite products of finite groups with J. Zapletal, accepted for publication in Confluentes Mathematici as of 6/28/2012.
Topological full groups of minimal subshifts and just-infinite groups accepted for publication in the Proceedings of the 12th Asian Logic Conference.
The bi-embeddability relation for finitely generated groups with J. Williams, accepted for publication in J. London Math. Soc.
A Descriptive View of Unitary Group Representations accepted for publication in J. Eur. Math. Soc..
The bi-embeddability relation for finitely generated groups II with J. Williams, accepted for publication in Arch. Math. Logic.
Invariant random subgroups of strictly diagonal limits of finite symmetric groups with R. Tucker-Drob, accepted for publication in Bull. London Math. Soc.
Invariant random subgroups of inductive limits of finite alternating groups with R. Tucker-Drob, accepted for publication in J. Algebra.
Characters of inductive limits of finite alternating groups accepted for publication in Ergodic Theory Dynam. Systems.
Uniformly recurrent subgroups of simple locally finite groups accepted for publication in Israel J. Math.
Complete groups are complete co-analytic accepted for publication in Arch. Math. Logic.
Topological full groups of minimal subshifts and the classification problem for finitely generated complete groups accepted for publication in Groups, Geometry, and Dynamics.
The bi-embeddability relation for countable abelian groups with F. Calderoni, accepted for publication in Trans. Amer. Math Soc.
On the E₀-extensions of countable Borel equivalence relations , preprint, August 2018.
Characters and invariant random subgroups of the finitary symmetric group , preprint, November 2018.
Diffuse invariant random subgroups , preprint 2022.
Realizing invariant random subgroups as stabilizer distributions , preprint 2022.
Diagonal embeddings of finite alternating groups , preprint 2022.

This page includes material based upon work supported by the National Science Foundation under successive grants including Grants No 9803417, 0100794, 0600940 and 1101597. Any opinions, findings, conclusions, or recommendations expressed herein are those of the authors and do not necessarily reflect the views of the National Science Foundaion.