6 papers
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…
Equicontinuous mappings on finite trees
Gerardo Acosta, David Fernández-Bretón
If is a finite tree and is a map, as the Main Theorem of this paper we find eight conditions, each of which is equivalent to the fact that is…
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…