CATEGORICAL ABSTRACT ALGEBRALIC LOGIC : PROTOALGEBRAICITY AND LEIBNIZ THEORY SYSTEMS
George Voutsadakis · Scientiae mathematicae Japonicae · 2005
Font and Jansana studied the Leibniz filters and the logic determined by the Leibniz filters of a given protoalgebraic sentential logic. A filter is Leibniz when it is the smallest among all the filters on the same algebra having the same Leibniz congruence. Inspired by their work, a study of the N-Leibniz theory systems of an N-protoalgebraic π-institution is initiated. A theory system is N-Leibniz if it is the smallest among all theory systems having the same Leibniz N-congruence system. In this study, some of the results of Font and Jansana on Leibniz filters are adapted to cover the case of N-protoalgebraic π-institutions. The N-Leibniz operator, used in the present setting, is the operator associating with a given theory family of a given π-institution the Leibniz N-congruence system of the theory family, as introduced in