Abstract.
Conditional equationally defined classes of many-sorted algebras, whose premises are conjunctions of (positive) equations and built-in predicates (constraints) in a basic first-order theory, are introduced. These classes are important in the field of algebraic specification because the combination of equational and built-in premises give rise to a type of clauses wich is more expressive than purely conditional equations. A sound and complete deductive system is presented and algebraic aspects of these classes are investigated. In particular, the existence of free algebras is examined.
