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Partitions of groups and matroids into independent subsets. (English) Zbl 1224.05084
Summary: Can the set $$\mathbb R\setminus\{0\}$$ be covered by countably many linearly (algebraically) independent subsets over the field $$\mathbb Q$$? We use a matroid approach to show that an answer is “Yes” under the continuum hypothesis, and “No” under its negation.

##### MSC:
 05B35 Combinatorial aspects of matroids and geometric lattices 05A18 Partitions of sets
##### Keywords:
matroid; partition; independent subset; continuum hypothesis
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