## Publications

Offprints available upon request.
1. (with Yash Lodha) A finitely presented group of piecewise projective homeomorphisms Groups Geometry and Dynamics 10 (2016), n 1, pp. 177--200.

2. 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. 171-187.

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

4. Amenability and Ramsey theory* Fund. Math. 220 (2013), n 3, pp. 263-280.

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

6. 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).

7. Model theory and the cardinal numbers $$\mathfrak{p}$$ and $$\mathfrak{t}$$* (commentary) Proc. Nat. Acad. Sci. 110 (2013), n 33, pp. 13238--13239.

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

9. (with David Aspero and Paul Larson) Forcing Axioms and the Continuum Hypothesis* Acta Mathematica. 210 (2013), n 1, pp. 1--29.

10. Forcing Axioms and the Continuum Hypothesis, part II: transcending $$\omega_1$$-sequences of reals* Acta Mathematica. 210 (2013), n 1, pp. 173--183.

11. (with Sławomir Solecki) A Boolean action of $$C(M,U(1))$$ without a spatial model.* Journal of Functional Analysis. 263 (2012), n 10, pp. 3224--3234.

12. (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).

13. (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).

14. The Proper Forcing Axiom* Proceedings of the 2010 meeting of the ICM. pp. 3--29

15. (with T. Ishiu) Minimality of non $$\sigma$$-scattered orders* Fundamenta Mathematicae. 205 (2009), n 1, pp. 29--44.

16. A Universal Aronszajn line* Mathematical Research Letters. 16 (2009), n 1, pp. 121--131.

17. (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 2--3, pp. 270--273.

18. Aronszajn lines and the club filter * Journal of Symbolic Logic. 73 (2008), n 3, pp. 1029--1035.

19. (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. 1--18.

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

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

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

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

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

25. $$\omega_1$$ and -$$\omega_1$$ may be the only minimal uncountable order types* Michigan Math. Journal 55 (2007), n 2, pp. 437--457.

26. A solution to the L space problem* Journal of the American Mathematical Society 19 (2006), n. 3, pp. 717--736.

27. The Proper Forcing Axiom, Prikry forcing, and the Singular Cardinals Hypothesis* Annals of Pure and Applied Logic 140 (2006), n 1--3, pp. 128--132.

28. A five element basis for the uncountable linear orders* Annals of Mathematics (2) 163 (2006), n 2, pp. 669--688.

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

30. Proper forcing, the continuum, and uncountable linear orders* Bulletin of Symbolic Logic, 11 (2005), n 1, pp. 51-60.

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

32. Weak diamond and open colorings Journal of Mathematical Logic, 3 (2003), n 1, pp. 119-125.

33. Random forcing and (S) and (L) Topology and its Applications, 131 (2003), n 2, pp. 139-148.

34. Open colorings, the continuum, and the second uncountable cardinal Proceedings of the American Mathematical Society, 130 (2002), n 9, pp. 2753-2759.

35. Continuous colorings associated with certain characteristics of the continuum , Discrete Math, 214 (2000), n 1-3, pp. 263-273.

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

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

38. (with D. K. Burke) Subspaces of the Sorgenfrey Line , Topology and its Applications, 90 (1998), n 1-3, pp. 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 grants: DMS-0401893, DMS-0200671, DMS-0757507, DMS-1262019.

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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