Dr Ross Brady has worked extensively on the consistency of naive set theory and its extension to higher order predicate theory, thus providing a logical solution to the set-theoretic and semantic paradoxes. He has subsequently worked on the proof theory of relevant logics, especially Gentzen systems and natural deduction. He has more recently specialized in the logic MC of meaning containment, setting it up as the logic of choice. He has studied metacompleteness and its associated logics, establishing properties for them that significantly diverge from those of classical logic. Indeed, he has recently proved the simple consistency of arithmetic by finitary methods, in contrast with Godel's celebrated Second Theorem.