7 citations · 26 across the 13 of their papers we have counts for
10 papers · 1 filter
Finitely additive measures on and additive combinatorics
Zeinab Ashtab, David Fernández-Bretón
We study (bounded) finitely additive measures on the group of integers , as elements of the Banach algebra , viewed as a natural generalization o…
-Ramsey ultrafilters
José Antonio Corona-García, David José Fernández-Bretón, Ulises Ariet Ramos-García
We study -Ramsey ultrafilters, ultrafilters containing witnesses to every shift-invariant instance of Ramsey's theorem. We prove that it is consistent that there are no…
Finiteness classes arising from Ramsey-theoretic statements in set theory without choice
Joshua Brot, Mengyang Cao, David Fernández-Bretón
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…
Generalized pathways
David J. Fernández-Bretón
We study a type of object, called a pathway (generalizing pathways in the sense of P. E. Cohen [Proc. Amer. Math. Soc. 74, No. 2 (1979), 318--321]), which is useful for several set…
Stable ordered union ultrafilters and
David José Fernández-Bretón
A union ultrafilter is an ultrafilter over the finite subsets of that has a base of sets of the form , where is an infinite pairwise disjoint family and $\m…
Hindman-like theorems with uncountably many colours and finite monochromatic sets
David Fernández-Bretón, Sung Hyup Lee
A particular case of the Hindman--Galvin--Glazer theorem states that, for every partition of an infinite abelian group into two cells, there will be an infinite …
A parametrized diamond principle and union ultrafilters
David Fernández-Bretón, Michael Hrušák
We consider a cardinal invariant closely related to Hindman's theorem. We prove that this cardinal invariant is small in the iterated Sacks perfect set forcing model, and that its…
A Characterization of the Boolean Prime Ideal Theorem in Terms of Forcing Notions
David Fernández-Bretón, Elizabeth Lauri
For certain weak versions of the Axiom of Choice (most notably, the Boolean Prime Ideal theorem), we obtain equivalent formulations in terms of partial orders, and filter-like obje…
Strong failures of higher analogs of Hindman's theorem
David Fernández-Bretón, Assaf Rinot
We show that various analogs of Hindman's Theorem fail in a strong sense when one attempts to obtain uncountable monochromatic sets: Theorem 1: There exists a colouring $c:\mathbb…
Gruff Ultrafilters
David Fernández-Bretón, Michael Hrušák
We investigate the question of whether carries an ultrafilter generated by perfect sets (such ultrafilters were called gruff ultrafilters by van Douwen). We prove that…