Matroids with an infinite circuit-cocircuit intersection
  We construct some matroids that have a circuit and a cocircuit with infinite intersection.   This answers a question of Bruhn, Diestel, Kriesell, Pendavingh and Wollan. It further shows that the axiom system for matroids proposed by Dress does not axiomatize all infinite matroids. We show that one of the matroids we define is a thin sums matroid whose dual isn't a thin sums matroid. 
Johannes Carmesin and Nathan Bowler
math.CO