I know that finitary matroids are those which can have potentially infinite ground sets yet have an additional axiom regarding additional axiom. I was wondering if there are any widely used terms for the family of subsets of an infinite ground set just satisfying the finite matroid axioms?
2026-03-25 14:07:57.1774447677
Is there a name for a family of subsets which satisfies the finite matroid axioms and the ground set is infinite?
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Oxley calls those pre-independence spaces, see e.g. https://www.math.lsu.edu/~oxley/infinitematroidschapter.pdf