Department of Mathematics
Boise State University
1910 University Drive
Boise, ID 83725-1555
- Set theory, especially Forcing Axioms, Determinacy, Large Cardinals, Fine structure theory, Infinitary combinatorics.
- Combinatorics, especially its interactions with mathematical logic.
Some of the entries below are based upon work supported by the National Science Foundation under grant DMS-0801189. 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.
- Set theory and its applications, L. Babinkostova, A. E. Caicedo, S. Geschke, M. Scheepers, eds., Contemporary Mathematics, vol. 533, Amer. Math. Soc., Providence, RI, 2011. MR2777741.
- Square principles in extensions, with Paul Larson, Grigor Sargsyan, Ralf Schindler, John Steel, and Martin Zeman. ArXiv. Submitted to the Israel Journal of Mathematics.
- Downward transference of mice and universality of local core models, with Martin Zeman. ArXiv. To appear in The Journal of Symbolic Logic.
- Definability of small puncture sets, with John Clemens, Clinton Conley, and Benjamin Miller. Fundamenta Mathematicae 215 (1) (2011), 39-51. MR2851700.
- and projective well-orderings of the reals, with Sy Friedman. The Journal of Symbolic Logic 76 (4) (2011), 1126-1136. MR2895389.
- A trichotomy theorem in natural models of , with Richard Ketchersid, in Set Theory and Its Applications, Contemporary Mathematics, vol. 533, Amer. Math. Soc., Providence, RI, 2011, pp. 227-258. MR2777751.
- Cardinal preserving elementary embeddings, in Logic Colloquium 2007, Françoise Delon, Ulrich Kohlenbach, Penelope Maddy, Frank Stephan, eds., Lecture Notes in Logic, Cambridge University Press – ASL (2010), 14-31. MR2668226.
- Regressive functions on pairs. European Journal of Combinatorics 31 (3) (2010), 803–812. MR2587031.
- Goodstein’s function, Revista Colombiana de Matemáticas 41 (2) (2007), 381-391. MR2585906.
- Projective well-orderings of the reals, with Ralf Schindler, Archive for Mathematical Logic 45 (7) (2006), 783-793. MR2266903.
- Real-valued measurable cardinals and well-orderings of the reals, in Set Theory. Centre de Recerca Matemàtica Barcelona, 2003-2004, Joan Bagaria, Stevo Todorcevic, eds., Trends in Mathematics, Birkhäuser (2006), 83-120. See also this note. MR2267147.
- The bounded proper forcing axiom and well-orderings of the reals, with Boban Velickovic. Mathematical Research Letters 13 (3) (2006), 393-408. MR2231126.
- Projective well-orderings and bounded forcing axioms, The Journal of Symbolic Logic 70 (2) (2005), 557-572. MR2140046.
- Exponenciación de cardinales infinitos, Lecturas Matemáticas 19 (2) (1998), 87-125. MR1856205.
- Simply definable well-orderings of the reals, Dissertation, UC Berkeley, 2003 (Advisors: John Steel, Hugh Woodin). MR2705176 (Wisest to ignore Chapter 4.)
- El problema de los cardinales singulares, Apuntes Matemáticos 37, Departamento de Matemáticas, Universidad de los Andes, Bogotá, 1996 (This is a reprint of my undergraduate dissertation, written under the supervision of Xavier Caicedo).
- Constructing -morasses for , by Bernhard Irrgang. To appear in Mathematical Reviews MR2850762.
- Proposing -morasses for , by Bernhard Irrgang. To appear in Mathematical Reviews MR2827553.
- The realm of the infinite, by W. Hugh Woodin. To appear in Mathematical Reviews MR2767235.
- On guessing generalized clubs at the successors of regulars, by Assaf Rinot. Mathematical Reviews MR2781096 (2012f:03105).
- A Dedekind finite Borel set, by Arnold W. Miller. Mathematical Reviews MR2765632 (2012f:03101).
- The two-cardinal problem for languages of arbitrary cardinality, by Luis Miguel Villegas Silva. Mathematical Reviews MR2723767 (2011m:03064).
- Generic embeddings associated to an indestructibly weakly compact cardinal, by Gunter Fuchs. Mathematical Reviews MR2720661 (2011m:03094).
- On coding uncountable sets of reals, by Joan Bagaria and Vladimir Kanovei. Mathematical Reviews MR2681346 (2011h:03109).
- More on regular and decomposable ultrafilters in ZFC, by Paolo Lipparini. Mathematical Reviews MR2681340 (2012f:03099).
- The consistency strength of the tree property at the double successor of a measurable cardinal, by Natasha Dobrinen and Sy Friedman. Mathematical Reviews MR2640069 (2011h:03106).
- On changing coﬁnality of partially ordered sets, by Moti Gitik. Mathematical Reviews MR2648158 (2011g:03112).
- Strong logics of first and second order, by Peter Koellner. Mathematical Reviews MR2656116 (2011e:03016).
- Cardinal characteristics and projective wellorders, by Vera Fischer and Sy Friedman. Mathematical Reviews MR2601019 (2011h:03100) .
- The determinacy of long games, by Itay Neeman. The Bulletin of Symbolic Logic 12 (2) (2006), 299-302.
- Determinacy and Jónsson cardinals, version of April 9, 2012.
- Woodin’s proof of the second incompleteness theorem for set theory. November 4, 2010.
- A linear algebra proof of the fundamental theorem of algebra, May 18, 2010.
- Defining non-empty small sets from families of finite sets, with John Clemens, Clinton Conley, and Benjamin Miller. December 4, 2009.
- On Real-valued measurability and Lebesgue measurable sets, October 11, 2005.
- A review of sharps, version of November 2004.
- Is Turing equivalence universal?, version of August 2004.