2 citations · 2 across the 4 of their papers we have counts for
4 papers
Folkman's theorem and the primes
David J. Fernández-Bretón
We provide two new proofs of the infinitude of prime numbers, using the additive Ramsey-theoretic result known as Folkman's theorem (alternatively, one can think of these proofs as…
The adjacent Hindman's theorem and the -Ramsey's theorem
Bruno Fernando Aceves-Martínez, David J. Fernández-Bretón, L. F. Romero-García +1
We consider the restriction of Ramsey's theorem that arises from considering only translation-invariant colourings of pairs, and show that this has the same strength (both from the…
Owings-like theorems for infinitely many colours or finite monochromatic sets
David J. Fernández-Bretón, Eliseo Sarmiento Rosales, Germán Vera
Inspired by Owings's problem, we investigate whether, for a given an Abelian group and cardinal numbers , every colouring yields a subset $X\subseteq…
Hindman's Theorem in the hierarchy of Choice Principles
David J. Fernández-Bretón
In the context of , we analyze a version of Hindman's finite unions theorem on infinite sets, which normally requires the Axiom of Choice to be proved. We establish th…