A class of algebraic theories called "recursion-closed," which generalize the rational theories studied by J. investigated. This work is motivated by the problem of providing the semantics of arbitrary polyadic recursion schemes in the framework of algebraic theories. It is suggested by Goguen et al. ("Proceedings, 17th IEEE Symposium") that the semantics of arbitrary polyadic recursion schemes can be handled using algebraic theories. The results show that this is indeed the case, but that

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... onal theories" are insufficient and that it is necessary to introduce a new class of "recursion-closed" algebraic theories. This new class of algebraic theories, is defined and studied, and "free recursion-closed algebraic theories" are proved to exist.