In the terminology of Anderson and Belnap (1975), an entailment connective -~ expresses relevant entailment only if A B holds only if B is relevant to A; and an if then connective ' expresses relevant implication only if A * B holds only if B is relevant to A. It is well known that the entailment connective of Lewis' modal logic, -8, does not express relevant entailment; for A A A -8 B and A -a B v B are provable in all the Lewis systems, where A and B are any formulae. Similarly material implication, D, does not express relevant implication in view of the validity of A A D A B and A D B v ~ B. Systems of relevant entailment and relevant implication are currently the subject of intensive research. Work centres on systems neighbouring the system H' of relevant entailment due to Ackermann (1956), in particular the system R of relevant implication due to Anderson and Belnap, and the system NR of relevant entailment due to Meyer. (NR is sometimes known as R".) Routley and Meyer (1972a, 1972b, 1973) set out model theoretic semantics for various relevant logics, in particular the systems R and NR. The semantics develop earlier ideas of Routley and Routley (1972). The essence of the approach is the use in the model theory of a group of structures broader than the set of all possible worlds. These structures are named "set ups" by the Routleys. The key feature of a set up is that, unlike a world, the set of sentences determined by it may be either or both inconsistent and negation incomplete: an arbitrary formula and its negation may both hold, or both fail to hold, in some set up. The set of worlds is strictly included in the set of set ups: a world is a consistent and negation complete set up. This key feature of set ups provides an easy way of falsifying the Lewis paradoxes AA ~ A B and B -* A v~ A (henceforward referred to as (P1) and (P2), respectively). The first is falsified in an inconsistent set up in which both A and ~ A hold but B fails, and the second in an incomplete set up in which B holds but both of A and ~A fail. A feature of Ackermann-style relevant entailment systems which has