We call a class M of matroids hereditary if it is closed under flats. We denote by Mᵉˣᵗ the class of matroids M that is in M, or has an element e such that M e is in M. We prove that if M has finitely many forbidden flats, then so does Mᵉˣᵗ.
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Singh et al. (2024) studied this question.
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