Publications

Offprints available upon request.
  1. Some remarks on the Open Coloring Axiom Ann. Pure Appl. Logic 172, 2021, n5, paper no. 102912, 6pp.
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  2. (with C. Bleak, M. Brin) Complexity among the finitely generated subgroups of Thompson's group J. Comb. Algebra 5, 2021, n1, 1–58.
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  3. A brief introduction to amenable equivalence relations to appear in a volume of Contemporary Mathematics.
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  4. Nonexistence of idempotent means on free binary systems Canadian Mathematical Bulletin 62 (2019), n3, 577–581.
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  5. (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.
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  6. (with Hossein Lamei Ramandi) There may be no minimal non \(\sigma\)-scattered linear orders* Math Research Letters 25 (2018), n6, 1957–1975.
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  7. (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.
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  8. What makes the continuum \(\aleph_2\)* Contemporary Math 690 (2017), 259–287.
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  9. (with Yash Lodha) A finitely presented group of piecewise projective homeomorphisms* Groups Geometry and Dynamics 10 (2016), n1, 177–200.
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  10. 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.
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  11. (with Alan Dow) Tightness in \(\sigma\)-compact spaces* Topology Proceedings 46 (2015), 213–232.

  12. 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\"oder-Heister, editors, College Publications (2015).
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  13. A Zorn's Lemma proof of the Dimension Theorem for vector spaces* American Mathematical Monthly 121 (2014), 260–262.
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  14. Amenability and Ramsey theory* Fund. Math. 220 (2013), n3, 263–280.
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  15. Fast growth in the Følner function for Thompson's group F * Groups, Geometry, and Dynamics 7 (2013), n 3, 633–651.
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  16. Model theory and the cardinal numbers \(\mathfrak{p}\) and \(\mathfrak{t}\)* (commentary) Proc. Nat. Acad. Sci. 110 (2013), n33, 13238–13239.
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  17. (with David Aspero and Paul Larson) Forcing Axioms and the Continuum Hypothesis* Acta Mathematica. 210 (2013), n1, 1–29.
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  18. Forcing Axioms and the Continuum Hypothesis, part II: transcending \(\omega_1\)-sequences of reals* Acta Mathematica. 210 (2013), n1, 173–183.
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  19. (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).
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  20. (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).
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  21. (with Sławomir Solecki) A Boolean action of \(C(M,U(1))\) without a spatial model.* Journal of Functional Analysis. 263 (2012), n10, 3224–3234.
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  22. (Fall 2012: prospective) Thematic Program on Forcing and its Applications* Fields Notes. 12:2 (2012), pages 4, 18.
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  23. The Proper Forcing Axiom* Proceedings of the 2010 meeting of the ICM. 3–29
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  24. (with T. Ishiu) Minimality of non \(\sigma\)-scattered orders* Fundamenta Mathematicae. 205 (2009), n1, 29–44.
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  25. A Universal Aronszajn line* Mathematical Research Letters. 16 (2009), n1, 121–131.
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  26. (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.
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  27. Aronszajn lines and the club filter * Journal of Symbolic Logic. 73 (2008), n3, 1029–1035.
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  28. (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.
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  29. An L space with a d-separable square* Topology and its Applications 155 (2008), 304–307.
    Electronic offprints are available upon request.

  30. Structural analysis of Aronszajn trees * Proceedings of the 2005 Logic Colloquium in Athens, Greece (2007), 85–106.
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  31. (with S. Todorcevic) The metrization problem for Frechet groups * in Open Problems in Topology II (E. Pearl, ed.), Elsevier (2007).
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  32. (with G. Gruenhage) Perfect compacta and basis problems in topology * in Open Problems in Topology II (E. Pearl, ed.), Elsevier (2007).
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  33. Compact spaces with hereditarily normal squares * to be included in Open Problems in Topology II (E. Pearl, ed.), Elsevier (2007).
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  34. \(\omega_1\) and -\(\omega_1\) may be the only minimal uncountable order types* Michigan Math. Journal 55 (2007), n2, 437–457.
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  35. A solution to the L space problem* Journal of the American Mathematical Society 19 (2006), n3, 717–736.
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  36. The Proper Forcing Axiom, Prikry forcing, and the Singular Cardinals Hypothesis* Annals of Pure and Applied Logic 140 (2006), n1–3, 128–132.
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  37. A five element basis for the uncountable linear orders* Annals of Mathematics (2) 163 (2006), n2, 669–688.
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  38. Set mapping reflection* Journal of Mathematical Logic, 5 (2005), n1, 87–98.
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  39. Locally compact locally countable spaces and random reals Topology and its Applications, 151 (2005), 169–179.
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  40. Proper forcing, the continuum, and uncountable linear orders* Bulletin of Symbolic Logic, 11 (2005), n1, 51–60.
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  41. Parametrized diamond principles Transactions of the American Mathematical Society, 356 (2004) 2281-2306.
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  42. Weak diamond and open colorings Journal of Mathematical Logic, 3 (2003), n1, 119–125.
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  43. Nonexistence of idempotent means on free binary systems accepted in Canadian Mathematical Bulletin
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  44. pdf file
  45. Random forcing and (S) and (L) Topology and its Applications, 131 (2003), n2, 139–148.
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  46. Open colorings, the continuum, and the second uncountable cardinal Proceedings of the American Mathematical Society, 130 (2002), n9, 2753–2759.
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  47. Continuous colorings associated with certain characteristics of the continuum , Discrete Math, 214 (2000), n1–3, 263–273.
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  48. A Linearly Fibered Souslinean Space Under MA , Topology Proceedings, 24 (1999), 233–247.
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  49. Some of the Combinatorics Related to Michael's Problem , Proceedings of the American Mathematical Society, 127 (1999), n 8, pp. 2459-2467.
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  50. (with D. K. Burke) Subspaces of the Sorgenfrey Line , Topology and its Applications, 90 (1998), n1–3, 57–68.
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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.

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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