David J. Fernández-Bretón

dblp:216/5365 · DBLP profile ↗
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3ranked-venue papers
2as first author
2since 2021 · last 2024
0000-0001-8084-055XORCID · corroborated

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Theory of computation · 3 · 2 first-author · 2 since 2021
YearPublicationVenuePosition
2024 Owings-like theorems for infinitely many colours or finite monochromatic sets
David J. Fernández-Bretón, Eliseo Sarmiento Rosales, Germán Vera
Ann. Pure Appl. Log.1
2021 Finiteness classes arising from Ramsey-theoretic statements in set theory without choice
Joshua Brot, Mengyang Cao, David J. Fernández-Bretón
Ann. Pure Appl. Log.3
2019 STABLE ORDERED UNION ULTRAFILTERS AND cov $\left( \mathcal{M} \right) < \mathfrak{c}$
abstract
Abstract A union ultrafilter is an ultrafilter over the finite subsets of ω that has a base of sets of the form ${\text{FU}}\left( X \right)$ , where X is an infinite pairwise disjoint family and ${\text{FU}}(X) = \left\{ {\bigcup {F|F} \in [X]^{ < \omega } \setminus \{ \emptyset \} } \right\}$ . The existence of these ultrafilters is not provable from the $ZFC$ axioms, but is known to follow from the assumption that ${\text{cov}}\left( \mathcal{M} \right) = \mathfrak{c}$ . In this article we obtain various models of $ZFC$ that satisfy the existence of union ultrafilters while at the same time ${\text{cov}}\left( \mathcal{M} \right) = \mathfrak{c}$ .
David J. Fernández-Bretón
J. Symb. Log.1