Varieties of many-sorted recognizable sets
Saeed Salehi, Magnus Steinby · 2007
We consider varieties of recognizable subsets of many-sorted finitely generated free algebras over a given variety, varieties of congruences of such al- gebras, and varieties of finite many-sorted algebras. A variety theorem that es- tablishes bijections between the classes of these three types of varieties is proved. For this, appropriate notions of many-sorted syntactic congruences and algebras are needed. Also an alternative type of varieties is considered where each subset consists of elements of just one sort.