On problem of existance of finite bases of identities, defining manifolds generated by recursive functions algebras

Abstract

A negative solution to the problem of the existence of finite bases is obtained identities defining varieties generated by algebras of unary recursive functions. It is shown that in varieties of algebras generated by algebras of primitive recursive and partially recursive functions, not there are finite bases of identities that define these varieties. For the algebra of unary general recursive functions, which is partial, a similar problem is solved in Kleene's semantics for identities.