David Fernández Bretón earned a Ph.D. from the Department of Mathematics and Statistics of York University in Toronto, under the supervision of Juris Steprāns.

My main interests are Logic and Set Theory, especially Forcing and Large Cardinals (although my knowledge of the latter is not as deep as I would like), and their applications to Algebra and Analysis. I am currently working on the algebra and topology of the Stone-Čech compactification of groups, notably Abelian groups, and with idempotents in said compactification. I have also been interested in the Cardinal Invariants of the Continuum for a while.

In a much more informal fashion (pretty much as a hobby), I also like to look at alternative axiomatizations of set theory, such as NFU, and some (very basic) category theory. I am also interested in the Philosophy of Mathematics and in Ludwig Wittgenstein’s life and work.

Personal website


Recent and upcoming talks by David J. Fernández Bretón

David J. Fernández Bretón: Strong failures of higher analogs of Hindman’s theorem, II

Thursday, October 20, 2016, from 4 to 5:30pm East Hall, room 3096 Speaker: David J. Fernández Bretón (University of Michigan) Title: Strong failures of higher analogs of Hindman’s theorem, II Abstract: (One of the versions of) Hindman’s theorem states that, whenever we partition an infinite abelian group G in two cells, there exists an infinite subset X of G such that the set FS(X) consisting of all sums of finitely many distinct elements of X is entirely contained within one of the cells of the partition. continue reading…

David J. Fernández Bretón: Strong failures of higher analogs of Hindman’s theorem, I

Thursday, October 13, 2016, from 4 to 5:30pm East Hall, room 3096 Speaker: David J. Fernández Bretón (University of Michigan) Title: Strong failures of higher analogs of Hindman’s theorem, I Abstract: (One of the versions of) Hindman’s theorem states that, whenever we partition an infinite abelian group G in two cells, there exists an infinite subset X of G such that the set FS(X) consisting of all sums of finitely many distinct elements of X is entirely contained within one of the cells of the partition. continue reading…

Set Theory and its Applications in Topology, September 11-16, 2016

The meeting took place in Oaxaca, Mexico. The slides may be found below. 08:45 – 09:00 Introduction and Welcome (Conference Room San Felipe) 09:00 – 10:00 Alan Dow: The even numbered problems (Conference Room San Felipe) 10:00 – 10:30 Rodrigo Jesus Hernandez Gutierrez: Spaces discretely generated at infinity (Conference Room San Felipe) 10:30 – 11:00 Coffee Break (Conference Room San Felipe) 11:00 – 11:30 Isván Juhász: Lindelöf spaces of countable pseudocharacter (Conference Room San Felipe) 11:30 – 12:00 Juris Steprans: PID and universal graphs (Conference Room San Felipe) 13:20 – 13:30 Group Photo (Hotel Hacienda Los Laureles) 13:30 – 15:00 Lunch (Restaurant Hotel Hacienda Los Laureles) 15:00 – 16:00 Itay Neeman: Forcing one instance of the Moore-Todorcevic principle (Conference Room San Felipe) 16:00 – 16:30 Coffee Break (Conference Room San Felipe) 16:30 – 17:00 James Cummings: Dowker and super-Dowker filters (Conference Room San Felipe) 17:00 – 17:30 Assaf Rinot: The $\omega_2$-Souslin problem (Conference Room San Felipe) 19:00 – 21:00 Dinner (Restaurant Hotel Hacienda Los Laureles) Tuesday, September 13 07:30 – 09:00 Breakfast (Restaurant at your assigned hotel) 09:00 – 10:00 Christina Brech: Bases of Homogeneous families bellow the first Mahlo cardinal (Conference Room San Felipe) 10:30 – 11:00 Coffee Break (Conference Room San Felipe) 11:00 – 11:30 Piotr Koszmider: A non-commutative Mrówka’s $\Psi$-space (Conference Room San Felipe) 11:30 – 12:00 Asger Tornquist: Invariant descriptive set theory and almost disjointness modulo an ideal (Conference Room San Felipe) 13:30 – 15:00 Lunch (Restaurant Hotel Hacienda Los Laureles) 15:00 – 16:00 Alexander Shibakov: Sequential groups: large and small (Conference Room San Felipe) 16:00 – 16:30 Coffee Break (Conference Room San Felipe) 16:30 – 17:00 Jindrich Zapletal: Strong measure zero sets in Polish groups (Conference Room San Felipe) 17:00 – 17:30 Marcin Sabok: On hyperfiniteness of boundary actions of hyperbolic groups (Conference Room San Felipe) 19:00 – 21:00 Dinner (Restaurant Hotel Hacienda Los Laureles) Wednesday, September 14 07:30 – 09:00 Breakfast (Restaurant at your assigned hotel) 09:00 – 09:30 Joerg Brendle: Q (Conference Room San Felipe) 09:30 – 10:00 Dilip Raghavan: More on the density zero ideal (Conference Room San Felipe) 10:00 – 10:30 Osvaldo Guzmán: Combinatorial properties of MAD families (Conference Room San Felipe) 10:30 – 11:00 Coffee Break (Conference Room San Felipe) 11:00 – 11:30 Victor Torres-Perez: Constructions with oppositions: Cardinal invariants and games (Conference Room San Felipe) 11:30 – 12:00 David Fernández Bretón: Strong failures of higher analogs of Hindman’s theorem (Conference Room San Felipe) 12:00 – 12:30 Natasha Dobrinen: Topological Ramsey spaces in some creature forcings (Conference Room San Felipe) 12:30 – 13:30 Lunch (Restaurant Hotel Hacienda Los Laureles) 13:30 – 17:30 Free Afternoon (Oaxaca) 19:00 – 21:00 Dinner (Restaurant Hotel Hacienda Los Laureles) Thursday, September 15 07:30 – 09:00 Breakfast (Restaurant at your assigned hotel) 09:00 – 10:00 Slawomir Solecki: Monoid actions on left-topological compact semigroups (Conference Room San Felipe) 10:30 – 11:00 Coffee Break (Conference Room San Felipe) 11:00 – 11:30 Aleksandra Kwiatkowska: The Ramsey degree of the pre-pseudoarc (Conference Room San Felipe) 11:30 – 12:00 Dana Bartosova: Ultrafilter combinatorics in topological dynamics (Conference Room San Felipe) 13:30 – 15:00 Lunch (Restaurant Hotel Hacienda Los Laureles) 15:00 – 16:00 Jan van Mill: Erdős spaces (Conference Room San Felipe) 16:00 – 16:30 Coffee Break (Conference Room San Felipe) 16:30 – 17:00 Anush Tserunyan: Topological dimension and Baire category (Conference Room San Felipe) 17:00 – 17:30 Yinhe Peng: Weak network and the basis problem (Conference Room San Felipe) 19:00 – 21:00 Dinner (Restaurant Hotel Hacienda Los Laureles) Friday, September 16 07:30 – 09:00 Breakfast (Restaurant at your assigned hotel) 09:00 – 09:30 Jeffrey Bergfalk: Walks… (Conference Room San Felipe) 09:30 – 10:00 Iian Smythe: A local Ramsey theory for block sequences (Conference Room San Felipe) 10:00 – 10:30 Noé de Rancourt: Ramsey theory with and without the pigeonhole principle (Conference Room San Felipe) 10:30 – 11:00 Coffee Break (Conference Room San Felipe) 11:00 – 11:30 Claribet Piña: Topological partition relations for $\omega^2$ (Conference Room San Felipe) 11:30 – 12:00 Carlos Uzcategui: Bases and selectors for cofinal families of countable sets (Conference Room San Felipe) 12:00 – 12:30 Carlos Di Prisco: Graphs on the Cantor set (Conference Room San Felipe) 12:30 – 14:30 Lunch (Restaurant Hotel Hacienda Los Laureles)   continue reading…

David Fernández Bretón: Ultrafilters on the rationals generated by perfect sets

Place: Fields Institute (Room 210) Date: June 17th, 2016 (13:30-15:00) Speaker: David Fernandez Bretón Title: Ultrafilters on the rationals generated by perfect sets Abstract:  In a 1992 paper, van Douwen defined what he calls a “gruff ultrafilter”: an ultrafilter on the rational numbers which is generated by perfect (this is, closed and crowded) sets; and asked whether these ultrafilters exist, providing in the same paper a proof that they do if cov(M)=c. continue reading…

David Fernández Bretón: d=c implies that there are gruff ultrafilters

Thursday, February 25, 4:00-5:30 PM at CC Little 2502 (note the nonstandard building/room!!!) I will show a proof of the statement in the title. Recall that a gruff ultrafilter was defined by van Douwen to be an ultrafilter on the rational numbers with a base of perfect subsets (where perfect means both closed (in the topology inherited from the usual Euclidean one from the reals) and crowded (without isolated points)). continue reading…

David Fernández Bretón: Gruff ultrafilters in the Random model

Thursday, January 28, 4:00-5:30 PM at CC Little 2502 (note the nonstandard building/room!!!): A gruff ultrafilter (a concept introduced by van Douwen) is an ultrafilter on the rational numbers with a base of perfect subsets (where perfect means both closed (in the topology inherited from the usual Euclidean one from the reals) and crowded (without isolated points)). continue reading…

David Fernández Bretón: An introduction to weak diamonds, II

Thursday, November 19, 2015; 16:00-17:30; East Hall 3096 After having introduced the basics of weak diamond principles, we will show their usage with some examples: construction of a Suslin tree, of strongly summable ulrafilters, and of gruff ultrafilters. continue reading…

David Fernández Bretón: An introduction to weak diamonds

Thursday, November 5, 2015, 16:00-17:30, 3096 East Hall. I will introduce the basics of weak diamond principles, and show their usage with a couple of examples (construction of a Suslin tree and of a P-point). continue reading…

David Fernandez Breton: All that there is to know about gruff ultrafilters, II

Wednesday, September 23, 2015 — 16:00 to 17:30 — 3096 East Hall An ultrafilter on the rational numbers is gruff if it has a base of perfect (this is, closed and without isolated points) sets. continue reading…

David Fernández Bretón: All that there is to know about gruff ultrafilters

Wednesday, September 16, 2015 3096 East Hall 16:00-17:30. Gruff ultrafilters are ultrafilters on the rational numbers that have a basis of perfect sets (according to the usual Euclidean topology). I will explain what is known about their existence, and hopefully (if there’s enough time) finish with a theorem of M. continue reading…