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: Models of set theory with union ultrafilters and small covering of meagre

Thursday, February 15, 2018, from 4 to 5:30pm East Hall, room 3088 Speaker: David J. Fernández Bretón (University of Michigan) Title: Models of set theory with union ultrafilters and small covering of meagre Abstract: Union ultrafilters are ultrafilters that arise naturally from Hindman’s finite unions theorem, in much the same way that selective ultrafilters arise from Ramsey’s theorem, and they are very important objects from the perspective of algebra in the Cech–Stone compactification. continue reading…

2nd Pan Pacific International Conference on Topology and Applications, November 13–17, 2017

The 2nd Pan Pacific International Conference on Topology and Applications (2nd PPICTA) had a special session in Set Theory, to which we now provide the slides. (50min. talks) 1. David Chodounsky (Institute of Mathematics CAS) Sacks indestructible ultrafilters and the HL property 2. continue reading…

David J. Fernández Bretón: More Ramsey-theoretic statements: uncountably many colours, finite monochromatic sets

Thursday, December 7, 2017, from 4 to 5:30pm East Hall, room 3096 Speaker: David J. Fernández Bretón (University of Michigan) Title: More Ramsey-theoretic statements: uncountably many colours, finite monochromatic sets Abstract: Hindman’s theorem states that for every colouring of an infinite abelian group with finitely many colours, there will be an infinite set whose finite sums are monochromatic. continue reading…

David J. Fernández Bretón: Higher degree versions of the Central Sets Theorem, II

Thursday, October 26, 2017, from 4 to 5:30pm East Hall, room 3096 Speaker: David J. Fernández Bretón (University of Michigan) Title: Higher degree versions of the Central Sets Theorem, II Abstract: The Central Sets Theorem is a Ramsey-theoretic result due to Furstenberg, from 1981, and multiple generalizations of it (in a variety of different directions) have been proved afterwards (to the best of my knowledge, the currently most general statement is due to De, Hindman and Strauss in 2008, but there are also many relevant results due to Bergelson). continue reading…

David J. Fernández Bretón: Higher degree versions of the Central Sets Theorem

Thursday, October 12, 2017, from 4 to 5:30pm East Hall, room 3096 Speaker: David J. Fernández Bretón (University of Michigan) Title: Higher degree versions of the Central Sets Theorem Abstract: The Central Sets Theorem is a Ramsey-theoretic result due to Furstenberg, from 1981, and multiple generalizations of it (in a variety of different directions) have been proved afterwards (to the best of my knowledge, the currently most general statement is due to De, Hindman and Strauss in 2008, but there are also many relevant results due to Bergelson). continue reading…

Ultrafilters, Ramsey Theory and Dynamics, Villeurbanne, November 20-24, 2017

Ultrafilters, Ramsey Theory and Dynamics 20-24 Nov 2017 Villeurbanne (France) Description This week-long event, scheduled between November 20 and November 24, 2017 at the University of Lyon 1, is a combined school and workshop focusing primarily on the rich interactions between ultrafilters, topological dynamics and ergodic theory and applications to Ramsey theory. continue reading…

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 Fernández Bretón: Strong failures of higher analogs of Hindman’s theorem, IV

Thursday, November 3, 2016, from 4 to 5:30pm East Hall, room 3096 Speaker: David Fernández Bretón (University of Michigan) Title: Strong failures of higher analogs of Hindman’s theorem, IV Abstract: This is talk 4 out of 4. continue reading…