Monadic characterisation conjecture for frame matroids

A matroid is a finite set system with an independence structure, and a frame matroid is a matroid arising from a biased graph; the monadic second-order language of matroids is the language that permits quantification over elements and sets of elements, together with the matroid relations. Frame-matroid monadic characterisation conjecture. There is a sentence in the monadic second-order language of matroids which characterises the class of frame matroids. Frame matroids are minor-closed, but have infinitely many excluded minors, so this conjecture would require structural methods beyond an excluded-minor list.