This is the section of my webpage where you can download some of my manuscripts: notes about miscellaneous topics, slides from previous talks, etc. Most of the oldest things are written in Spanish, and most of the newest ones are in English (the items are ordered in reverse chronological order). If you would like to see my formal publications, click on Publications.
Notes
When I was at the University of Michigan, I taught an introductory course to set theory (MATH 582) three times, which gave me ample opportunity to compile the material that I used to teach that class (which wasn't based on any single textbook). The result is the following set of notes , which more or less faithfully reflects my view of how the topic should be learned. I'm extremely open to (and will be very grateful for) any comments or suggestions. I hope to be able to turn these (after some further completing and polishing) into a book some day.
One of the results of my paper (joint with Michael Hrušák) on Gruff ultrafilters had a serious mistake (discovered by Osvaldo Guzmán), which prompted us to eventually publish a corrigendum (in fact, the mistake in this paper can be traced back to an old paper of Paul E. Cohen (not to be confused with the Paul J. Cohen that discovered forcing!), thus turning the statement that there are P-points in the random model from a theorem back into an open problem). Attempts to fix that proof led me to formulating the definition of a "generalized pathway", a set-theoretic device whose existence allows to perform certain mathematical constructions in much the same way that assuming a certain a cardinal characteristic to be large does. All I know about these objects is written in this set of notes . I don't have any plans to try and publish this in the near future (there is still much work to be done before the notes are sufficiently valuable, and I'm currently mostly focused on other research projects), but some people have found them valuable, so I put them here (however, if you plan to cite these notes, it's probably more optimal to cite the arXiv version).
A set of notes (in Spanish) on club and diamond , two
well-known combinatorial principles of Set Theory. In order to
understand the last section, knowledge of the forcing technique is
required.
Back in my youth, I wrote some notes on ordinal numbers (in Spanish), including an interesting discussion on the Axiom of Infinity. (I used to have plans to complement these by adding a part on cardinal numbers, but by now it's clear that this is just non going to happen.)
Slides
Slides from my talk Independence proofs, what are they (good for)? (Pruebas de independencia: ¿Qué son y para qué sirven?), Mathematics Seminar, ESFM-IPN.
Slides from my talk Comparing the difficulty of combinatorial results using Mathematical Logic, which took place on May 18th., within the conference Interacciones en la Frontera 2021.
Slides from the first talk of the minicourse on Ramsey Theory and Applications, which took place on May 17th., within the conference Interacciones en la Frontera 2021.
Slides from the talk Set Theory (sometimes) can solve your problem!, which was my "Capsule Research Talk" (an annual series of short talks, at the Department of Mathematics, University of Michigan, given by the incoming postdocs in order to introduce the Department members to their research), August 31st., 2015.
Slides from the talk
On collectionwise Hausdorff spaces, which took place on November 4th., 2009, on the Seventh "Jornadas de Topología".
Slides from my talk
A problem of algebra which turned out to be undecidable, which took place on October 13th., 2009, at
the XLII National Congress of the Mexican Mathematical Society. My notes
on Whitehead's problem are the result of preparing this talk.
Slides from my talk
On Carmichael numbers, which took place on October 23th., 2008, at the
XLI National Congress of the Mexican Mathematical Society.
set of notes