On a categorical approach to the study of algorithmic algebras (Q1895010)

A class of algorithmic algebras in the sense of \textit{V. M. Glushkov}, \textit{G. E. Tseitlin} and \textit{E. L. Yushchenko} [Algebra. Languages. Programming (Russian) (1974; Zbl 0297.68054)], with data separation is introduced. Any algorithmic algebra \(A\) has a unique replica (interpreter) \(I(A)\) in this class. The algebra \(I(A)\) preserves some properties of the algebra \(A\). The special case of interpreters in categories of sets and metric compacts is considered. In the latter case it is shown that the data space of an interpreter is a Cantor perfect space which is a Stone space of the Boolean algebra of two-valued predicates of the interpreter.