Base partition for mixed families of finitary and cofinitary matroids

Abstract

Let $\mathcal{M}=(M_i:i\in K)$ be a finite or infinite family consisting of matroids on a common ground set $E$ each of which may be finitary or cofinitary. We prove the following Cantor-Bernstein-type result: If there is a collection of bases, one for each $M_i$, which covers the set $E$, and also a collection of bases which is pairwise disjoint, then there is a collection of bases which partitions $E$. We also show that the failure of this Cantor-Bernstein-type statement for arbitrary matroid families is consistent relative to the axioms of set theory ZFC.

References in corpus (1)

• The ubiquity of Psi-matroids