*239-A Mathematics/Geosciences building*

Department of Mathematics

Boise State University

Department of Mathematics

Boise State University

1910 University Drive

*Boise, ID 83725-1555*

`e-mail :`caicedo (at) math (dot) boisestate (dot) edu### Research Interests

- 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. *

### Contents: Books, Papers, Reviews, Notes.

### Books

**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.

### Papers

*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).

### Reviews

*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.

### Notes (typically not intended for publication)

- 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.

[...] accepted for publication in the Proceedings of the Logic Coloquium 2007. You can find it in my papers [...]

[...] of Goodstein’s function and issues related to independence in can be found in the old page for my undecidability course in [...]

[...] and definability I have made some changes to my webpage and now my papers can be found here, on a page in this [...]

[...] Algebra/Number Theory/Combinatorics Seminar on the topic of this paper, which can be found in my papers [...]

[...] is based on two recent papers of mine that can be found on my papers page: Regressive functions on pairs, that has been submitted to the European Journal of [...]

[...] theorem in natural models of to the Proceedings of BEST. The preprint is available at my papers page. In the paper we provide references and background for the results we discuss, so here I will [...]

[...] functions on pairs (For background, see my paper Regressive functions on pairs, in my papers [...]

[...] BPFA and projective well-orderings of the reals By andrescaicedo Sy Friedman and I recently submitted the paper and projective well-orderings of the reals to The Journal of Symbolic Logic. The preprint is available at my papers page. [...]

[...] the second part of a paper I mentioned here a while ago. The preprint is available at my papers [...]

[...] mice and universality of local core models to the Journal of Symbolic Logic, downloadable from my papers page. We have also uploaded it on the ArXiV, and I’ll add a link once it goes live. (I should [...]

[...] have posted a short note with the proof on my papers page. The note is hastily written, and I would [...]

[...] principles in extensions to the Israel Journal of Mathematics. The paper can be downloaded form my papers page, or from the arXiv (I will add a link once it goes [...]

[...] Notes and papers [...]