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We construct some matroids that have a circuit and a cocircuit with infiniteintersection.  This answers a question of Bruhn, Diestel, Kriesell, Pendavingh and Wollan.It further shows that the axiom system for matroids proposed by Dress does notaxiomatize all infinite matroids. We show that one of the matroids we define isa thin sums matroid whose dual isn't a thin sums matroid.

Matroids with an infinite circuit-cocircuit intersection