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: mathfrak p=mathfrak t, III

Tuesday, April 18, 2017, from 4 to 5:30pm East Hall, room 3096 Speaker: David J. Fernández Bretón (University of Michigan) Title: mathfrak p=mathfrak t, III Abstract: This is the third and last talk in the series (reasonably self-contained for those who missed any number of previous parts). continue reading…

David J. Fernández Bretón: mathfrak p=mathfrak t, II

Thursday, April 6, 2017, from 4 to 5:30pm East Hall, room 3088 Speaker: David J. Fernández Bretón (University of Michigan) Title: mathfrak p=mathfrak t, II Abstract: This is the second in a series of (hopefully at most) three talks, and it will be reasonably self-contained for those who missed the first part. continue reading…

David J. Fernández Bretón: mathfrak p=mathfrak t

Thursday, March 30, 2017, from 4 to 5:30pm East Hall, room 3088 Speaker: David J. Fernández Bretón (University of Michigan) Title: mathfrak p=mathfrak t Abstract: In a series of (hopefully at most) two talks, I will present the proof, due to Maryanthe Malliaris and Saharon Shelah in 2012, that the cardinal invariants p and t are equal, which constitutes an extremely important result in the theory of Cardinal Characteristics of the Continuum. continue reading…

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

Thursday, October 27, 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, III Abstract: Assuming the Continuum Hypothesis, Hindman, Leader and Strauss recently exhibited a colouring of the real line with two colours such that, for every uncountable set of reals, the collection of pairwise sums of these reals is panchromatic. continue reading…

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…

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…