In relevance logic it has become commonplace to associate with each logic both an algebraic counterpart and a relational counterpart. The former comes from the Lindenbaum construction; the latter, called a model structure, is designed for semantical purposes. Knowing that they are related through the logic, we may enquire after the algebraic relationship between the algebra and the model structure. This paper offers a complete solution for the relevance logic R. Namely, R-algebras and R-model structures can be obtained from each (...) other, and represented in terms of each other, by application of power constructions. (shrink)