Positive Structures

The paper reviews the current state of the theory of positive (or computably enumerable) structures. This theory is relevant to several branches of algebra, logic and computer science, e.g. to algorithmic problems in algebra, theory of quasivarieties, logic programming, algebraic specifications of data types. Along with the general theory of positive structures we consider also positive structures of special kind (the most interesting results are obtained for positive boolean algebras) and some appliations of positive structures to logic and computability theory.