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 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…

David Fernandez: A model of ZFC with strongly summable ultrafilters, small covering of meagre and large dominating number

Place: Fields Institute, Room 210 Date and time: Friday 23 January 2015 (13:30-15:00) Speaker: David Fernandez Title: A model of ZFC with strongly summable ultrafilters, small covering of meagre and large dominating number. continue reading…

David Fernandez: Two microcontributions to the theory of Strongly Summable Ultrafilters

4 April 2014, 13:30–15:00 Fields institute, Room 210 Speaker:  David Fernandez Title:  Two microcontributions to the theory of Strongly Summable Ultrafilters Strongly Summable Ultrafilters are those generated by FS-sets (where FS(X) is the set of all possible sums of finitely many elements from X (you can only add each element once)). continue reading…

David Fernandez: Strongly Productive Ultrafilters

04/October/2013, 13:30–15:00 Fields institute, Room 210 Speaker:  David Fernandez (York University) Title:  Strongly Productive Ultrafilters Abstract: The concept of a Strongly Productive Ultrafilter on a semigroup (known as a “strongly summable ultrafilter” when the semigroup is additively denoted) constitute an important concept ever since Hindman defined it, while trying to prove the theorem that now bears his name. continue reading…