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: Algebraic Ramsey-theoretic results with small monochromatic sets

BIU seminar in Set Theory November 5, 2018 Speaker: David J. Fernández Bretón (KGRC) Title: Algebraic Ramsey-theoretic results with small monochromatic sets Abstract: We will explore some (recent and not so recent; some positive, some negative) Ramsey-type results (each of which is due to some subset of the set {Komj\’ath, Hindman, Leader, H.S. continue reading…

David Fernández-Bretón: Finiteness classes arising from Ramsey-theoretic statements in set theory without choice

Talk held by David Fernández-Bretón (KGRC) at the KGRC seminar on 2018-10-04. The recorded talk is available here. Abstract: In the absence of the Axiom of Choice, there may be infinite sets for which certain Ramsey-theoretic statements – such as Ramsey’s or (appropriately phrased) Hindman’s theorem – fail. continue reading…

Joshua Brot, Mengyang Cao, David J. Fernández-Bretón: Finiteness classes arising from Ramsey-theoretic statements in set theory without choice

Thursday, June 14, 2018, from 4 to 5:30pm East Hall, room 4096 Speaker: Joshua Brot, Mengyang Cao, David J. Fernández-Bretón (University of Michigan) Title: Finiteness classes arising from Ramsey-theoretic statements in set theory without choice Abstract: We investigate infinite sets that witness the failure of certain Ramsey-theoretic statements, such as Ramsey’s or (appropriately phrased) Hindman’s theorem; such sets may exist if one does not assume the Axiom of Choice. continue reading…

David Fernández-Bretón: Variations and analogs of Hindman’s theorem

Mathematical logic seminar – May 22 2018 Time:     3:30pm – 4:30 pm Room:     Wean Hall 8220 Speaker:         David Fernández-Bretón Department of Mathematics University of Michigan Title:     Variations and analogs of Hindman’s theorem Abstract: Hindman’s theorem is a Ramsey-theoretic result asserting that, whenever one colours the set of natural numbers with finitely many colours, there will be an infinite set such that all numbers that can be obtained by adding finitely many elements from the set (no repetitions allowed) have the same colour. continue reading…

David Fernandez Breton: Partition theorems on uncountable abelian groups

Place: Fields Institute (Room 210) Date: April 27, 2018 (13:30-15:00) Speaker: David Fernandez Breton Title: Partition theorems on uncountable abelian groups Abstract: In the past two years, a number of Ramsey-theoretic results concerning the additive structure of uncountable abelian groups have been investigated by diverse subsets of the set {Komjáth, Rinot, D. continue reading…

David J. Fernández Bretón: Models of set theory with union ultrafilters and small covering of meagre, II

Thursday, March 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, II 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…

BLAST 2018, Denver, August 6-10, 2018

BLAST 2018 University of Denver, Colorado, USA August 6-10, 2018 The tenth-anniversary installment of BLAST will be held at the University of Denver from August 6 to August 10, 2018. Tutorial speakers: Paul Gartside (University of Pittsburgh) George Metcalfe (Universität Bern) Drew Moshier (Chapman University) Plenary speakers: Dana Bartosova (Carnegie Mellon University) Manuela Busaniche (National Scientific and Technical Research Council, Buenos Aires) Mirna Dzamonja (University of East Anglia, UK) David Fernandez-Breton (University of Michigan) Wesley Holliday (UC Berkeley) Agnes Szendrei (CU Boulder) Local organizing committee: Natasha Dobrinen Wesley Fussner Nick Galatos Dan Hathaway Gavin St. continue reading…

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…