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arXiv · 1910.05601

Base partition for mixed families of finitary and cofinitary matroids

Joshua Erde·Pascal Gollin·Attila Joó·Paul Knappe·Max Pitz
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Abstract

Let ${\mathcal{M} = (M_i \colon i\in K)}$ 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.

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Joshua Erde, Pascal Gollin, Attila Joó, Paul Knappe, Max Pitz. 2019-10-12. Base partition for mixed families of finitary and cofinitary matroids. https://doi.org/10.1007/s00493-020-4422-4

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