Recognisability for algebras of infinite trees (Q551167)

The author proposes an algebraic approach to the theory of regular languages of infinite trees that would parallel the classical semigroup-theoretic treatment of regular languages of finite words and the many later theories inspired by it. For this purpose he introduces a suitable class of algebras, called \(\omega\)-hyperclones, and proves then that the sets recognized by a certain special type of such algebras are precisely the regular languages of infinite trees. Furthermore, he presents some closure properties of these algebras from which the equivalence of recognizability and second-order definability also follows.