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 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…

David Fernández: Strongly summable ultrafilters and union ultrafilters are not the same thing

21/June/2013, 13:30–15:00 Fields institute,Room 210 Speaker: David J. Fernández Bretón Title: Strongly summable ultrafilters and union ultrafilters are not the same thing Abstract: This is, in some sense, a continuation of my previous talk (though of course self-contained). continue reading…

David Fernández: Every strongly summable ultrafilter is sparse

24/May/2013, 13:30–15:00 Fields institute,Room 210 Speaker: David J. Fernández Bretón Title: “Every strongly summable ultrafilter is sparse!” Abstract: The concept of a Strongly Summable Ultrafilter was born from Hindman’s efforts for proving the theorem that now bears his name (which at the time was known as Graham-Rothschild’s conjecture), although later on it got a life of its own and started to be studied for its own sake, mostly because of its nice algebraic properties. continue reading…