Publications

Electronic versions below are generally not the final version of the published work.
Offprints available upon request.

(with S. Solecki) The spectral form of Koopman representations of the group of measurable functions with values in the circle Colloquium Math. 171, 2023, n2, 303–320.

Rank-to-rank embeddings, Laver tables, and Galton-Watson processes Topology Appl. 323, 2023, paper no. 108292, 8pp.
Electronic offprints are available upon request.

Some remarks on the Open Coloring Axiom Ann. Pure Appl. Logic 172, 2021, n5, paper no. 102912, 6pp.

(with C. Bleak, M. Brin) Complexity among the finitely generated subgroups of Thompson's group J. Comb. Algebra 5, 2021, n1, 1–58.

A brief introduction to amenable equivalence relations in Trends in set theory, Contemporary Mathematics 752 (2020) 153–163

Nonexistence of idempotent means on free binary systems Canadian Mathematical Bulletin 62 (2019), n3, 577–581.

(with C. Bleak, M. Brin, M. Kassabov, M. Zaremsky) Groups of fast homeomorphisms of the interval and the ping-pong argument^* Journal of Combinatorial Algebra 3 (2019), n1, 11–40.

(with Hossein Lamei Ramandi) There may be no minimal non \(\sigma\)-scattered linear orders^* Math Research Letters 25 (2018), n6, 1957–1975.

(with Stevo Todorcevic) Baumgartner's isomorphism problem for \(\aleph_2\)-dense suborders of \(\mathbb{R}\)^* Archive for Mathematical Logic 56 (2017), n7–8, 1105–1114.

What makes the continuum \(\aleph_2\)^* Contemporary Math 690 (2017), 259–287.

(with Yash Lodha) A finitely presented group of piecewise projective homeomorphisms^* Groups Geometry and Dynamics 10 (2016), n1, 177–200.

Hindman's Theorem, Ellis's Lemma, and Thompson's group \(F\).^* Zbornik Radova of the Mathematical Institute of the Serbian Academy of Sciences and Arts 17 (2015), n25, 171–187.

(with Alan Dow) Tightness in \(\sigma\)-compact spaces^* Topology Proceedings 46 (2015), 213–232.

The utility of the uncountable.^* To be included in the proceedings of the 2011 Congress on Logic, Methodology, and the Philosophy of Science. Logic, Methodology and Philosophy of Science: Proceedings of the 14th International Congress., P. Edouard Bour, G. Heinzmann, W. Hodges, P. Schröder-Heister, editors, College Publications (2015).

A Zorn's Lemma proof of the Dimension Theorem for vector spaces^* American Mathematical Monthly 121 (2014), 260–262.

Amenability and Ramsey theory^* Fund. Math. 220 (2013), n3, 263–280.

Fast growth in the Følner function for Thompson's group F ^* Groups, Geometry, and Dynamics 7 (2013), n 3, 633–651.

Model theory and the cardinal numbers \(\mathfrak{p}\) and \(\mathfrak{t}\)^* (commentary) Proc. Nat. Acad. Sci. 110 (2013), n33, 13238–13239.

(with David Aspero and Paul Larson) Forcing Axioms and the Continuum Hypothesis^* Acta Mathematica. 210 (2013), n1, 1–29.

Forcing Axioms and the Continuum Hypothesis, part II: transcending \(\omega_1\)-sequences of reals^* Acta Mathematica. 210 (2013), n1, 173–183.

(with Todd Eisworth and David Milovich) Iterated forcing and the Continuum Hypothesis^* in Appalachian set theory 2006-2012, J. Cummings and E. Schimmerling, eds. London Math Society Lecture Notes series, Cambridge University Press (2013).

(with David Milovich) A tutorial on Set Mapping Reflection^* in Appalachian set theory 2006-2012, J. Cummings and E. Schimmerling, eds. London Math Society Lecture Notes series, Cambridge University Press (2013).

(with Sławomir Solecki) A Boolean action of \(C(M,U(1))\) without a spatial model.^* Journal of Functional Analysis. 263 (2012), n10, 3224–3234.

(Fall 2012: prospective) Thematic Program on Forcing and its Applications^* Fields Notes. 12:2 (2012), pages 4, 18.

The Proper Forcing Axiom^* Proceedings of the 2010 meeting of the ICM. 3–29

(with T. Ishiu) Minimality of non \(\sigma\)-scattered orders^* Fundamenta Mathematicae. 205 (2009), n1, 29–44.

A Universal Aronszajn line^* Mathematical Research Letters. 16 (2009), n1, 121–131.

(with S. Solecki) A \(G_\delta\) ideal of compact sets strictly above the nowhere dense ideal in the Tukey order ^* Annals of Pure and Applied Logic. 156 (2008), n2–3, 270–273.

Aronszajn lines and the club filter ^* Journal of Symbolic Logic. 73 (2008), n3, 1029–1035.

(with B. Koenig, P. Larson, B. Velickovic) Bounding the consistency strength of a five element linear basis^* Israel Journal of Mathematics. 164 (2008), n1, 1–18.

An L space with a d-separable square^* Topology and its Applications 155 (2008), 304–307.
Electronic offprints are available upon request.

Structural analysis of Aronszajn trees ^* Proceedings of the 2005 Logic Colloquium in Athens, Greece (2007), 85–106.

(with S. Todorcevic) The metrization problem for Frechet groups ^* in Open Problems in Topology II (E. Pearl, ed.), Elsevier (2007).

(with G. Gruenhage) Perfect compacta and basis problems in topology ^* in Open Problems in Topology II (E. Pearl, ed.), Elsevier (2007).

Compact spaces with hereditarily normal squares ^* to be included in Open Problems in Topology II (E. Pearl, ed.), Elsevier (2007).

\(\omega_1\) and -\(\omega_1\) may be the only minimal uncountable order types^* Michigan Math. Journal 55 (2007), n2, 437–457.

A solution to the L space problem^* Journal of the American Mathematical Society 19 (2006), n3, 717–736.

The Proper Forcing Axiom, Prikry forcing, and the Singular Cardinals Hypothesis^* Annals of Pure and Applied Logic 140 (2006), n1–3, 128–132.

A five element basis for the uncountable linear orders^* Annals of Mathematics (2) 163 (2006), n2, 669–688.

Set mapping reflection^* Journal of Mathematical Logic, 5 (2005), n1, 87–98.

Locally compact locally countable spaces and random reals Topology and its Applications, 151 (2005), 169–179.

Proper forcing, the continuum, and uncountable linear orders^* Bulletin of Symbolic Logic, 11 (2005), n1, 51–60.

Parametrized diamond principles Transactions of the American Mathematical Society, 356 (2004) 2281-2306.

Weak diamond and open colorings Journal of Mathematical Logic, 3 (2003), n1, 119–125.

Random forcing and (S) and (L) Topology and its Applications, 131 (2003), n2, 139–148.

Open colorings, the continuum, and the second uncountable cardinal Proceedings of the American Mathematical Society, 130 (2002), n9, 2753–2759.

Continuous colorings associated with certain characteristics of the continuum , Discrete Math, 214 (2000), n1–3, 263–273.

A Linearly Fibered Souslinean Space Under MA , Topology Proceedings, 24 (1999), 233–247.

Some of the Combinatorics Related to Michael's Problem , Proceedings of the American Mathematical Society, 127 (1999), n 8, pp. 2459-2467.

(with D. K. Burke) Subspaces of the Sorgenfrey Line , Topology and its Applications, 90 (1998), n1–3, 57–68.

The above entries marked with a * are subject to the following acknowledgment and disclaimer:

This material is based upon work supported by the National Science Foundation under one of the following NSF grants: DMS-0401893, DMS-0200671, DMS-0757507, DMS-1262019, DMS-1600635, DMS-1854367, DMS-2153975.

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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