Publications
Offprints available upon request.

What makes the continuum \(\aleph_2\)^{*}
Contemporary Math 690 (2017), pp. 259287.

(with Stevo Todorcevic) Baumgartner's isomorphism problem for \(\aleph_2\)dense suborders of \(\mathbb{R}\)^{*}
Archive for Mathematical Logic 56 (2017), n 78, pp. 11051114.

(with Yash Lodha)
A finitely presented group of piecewise projective homeomorphisms^{*}
Groups Geometry and Dynamics 10 (2016), n 1, pp. 177200.
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), n 25, pp. 171187.

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. Schr\"oderHeister, editors, College Publications (2015).

A Zorn's Lemma proof of the Dimension Theorem for vector spaces^{*}
American Mathematical Monthly
121 (2014), pp. 260262.

Amenability and Ramsey theory^{*}
Fund. Math.
220 (2013), n 3, pp. 263280.

Fast growth in the Følner function for Thompson's group F ^{*}
Groups, Geometry, and Dynamics
7 (2013), n 3, pp. 633651.

Model theory and the cardinal numbers \(\mathfrak{p}\) and \(\mathfrak{t}\)^{*} (commentary)
Proc. Nat. Acad. Sci.
110 (2013), n 33, pp. 1323813239.

(with David Aspero and Paul Larson) Forcing Axioms and the Continuum Hypothesis^{*}
Acta Mathematica.
210 (2013), n 1, pp. 129.

Forcing Axioms and the Continuum Hypothesis, part II:
transcending \(\omega_1\)sequences of reals^{*}
Acta Mathematica.
210 (2013), n 1, pp. 173183.

(with Todd Eisworth and David Milovich) Iterated forcing and the Continuum Hypothesis^{*}
in Appalachian set theory 20062012, 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 20062012, 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), n 10, pp. 32243234.

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

The Proper Forcing Axiom^{*}
Proceedings of the 2010 meeting of the ICM. pp. 329
 (with T. Ishiu)
Minimality of non \(\sigma\)scattered orders^{*}
Fundamenta Mathematicae.
205 (2009), n 1, pp. 2944.

A Universal Aronszajn line^{*}
Mathematical Research Letters.
16 (2009), n 1, pp. 121131.
 (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), n 23, pp. 270273.

Aronszajn lines and the club filter ^{*}
Journal of Symbolic Logic.
73 (2008), n 3, pp. 10291035.
 (with B. Koenig, P. Larson, B. Velickovic)
Bounding the consistency strength of a five element linear basis^{*}
Israel Journal of Mathematics.
164 (2008), n 1, pp. 118.

An L space with a dseparable square^{*}
Topology and its Applications
155 (2008), pp. 304307.
Electronic offprints are available upon request.

Structural analysis of Aronszajn trees ^{*}
Proceedings of the 2005 Logic Colloquium in Athens, Greece
(2007), 85106.

(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), n 2, pp. 437457.

A solution to the L space problem^{*}
Journal of the American Mathematical Society
19 (2006), n. 3, pp. 717736.

The Proper Forcing Axiom, Prikry forcing, and
the Singular Cardinals Hypothesis^{*}
Annals of Pure and Applied Logic
140 (2006), n 13, pp. 128132.

A five element basis for the uncountable linear orders^{*}
Annals of Mathematics (2)
163
(2006), n 2, pp. 669688.

Set mapping reflection^{*}
Journal of Mathematical Logic,
5
(2005), n 1, pp. 8798.

Locally compact locally countable spaces and random reals
Topology and its Applications,
151
(2005), pp. 169179.

Proper forcing, the continuum,
and uncountable linear orders^{*}
Bulletin of Symbolic Logic,
11
(2005), n 1, pp. 5160.
 Parametrized diamond principles
Transactions of the American Mathematical Society,
356
(2004) pp. 22812306.
 Weak diamond and open colorings
Journal of Mathematical Logic,
3
(2003), n 1, pp. 119125.

Random forcing and (S) and (L)
Topology and its Applications,
131
(2003), n 2, pp. 139148.
 Open colorings, the continuum, and the second uncountable cardinal
Proceedings of the American Mathematical Society,
130
(2002), n 9, pp. 27532759.

Continuous colorings associated with certain characteristics of the continuum ,
Discrete Math,
214
(2000), n 13, pp. 263273.

A Linearly Fibered Souslinean Space Under MA ,
Topology Proceedings,
24
(1999), pp. 233247.

Some of the Combinatorics Related to Michael's Problem ,
Proceedings of the American Mathematical Society,
127
(1999), n 8, pp. 24592467.
 (with D. K. Burke)
Subspaces of the Sorgenfrey Line ,
Topology and its Applications,
90
(1998), n 13, pp. 5768.
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: DMS0401893,
DMS0200671, DMS0757507, DMS1262019, DMS1600635.
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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