Categorical abstract algebraic logic: The Diagram and the Reduction Operator Lemmas

The study of structure systems, an abstraction of the concept of first‐order structures, is continued. Structure systems have algebraic systems as their algebraic reducts and their relational component consists of a collection of relation systems on the underlying functors. An analog of the expansion of a first‐order structure by constants is presented. Furthermore, analogs of the Diagram Lemma and the Reduction Operator Lemma from the theory of equality‐free first‐order structures are provided in the framework of structure systems. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)