Mayhew–Newman–Whittle finite rank-axiom conjecture for representable matroids

A representable matroid is a matroid satisfying the rank axioms of a matroid and representable over a field. Mayhew–Newman–Whittle conjecture. It is impossible to characterise the class of representable matroids with a finite number of rank axioms.

This conjecture concerns whether representability can be captured by finitely many additional rank inequalities beyond the three defining matroid rank axioms. The source attributes it to Mayhew, Newman, and Whittle and states that the problem remains open.