Sentences true in all constructive models

Abstract

Let P 0 , …,P q be predicates, of which at least one has two or more places. By a formula in P 0 , …, P q (or simply a formula , when the list P 0 , …, P q is fixed, as in this section) is meant any formula whose only symbols, other than sentential connectives, quantifiers, and (individual) variables, are among P 0 , …, P q . A realization (or possible model ) of such a formula is a system where A is a non-empty set and each P k is a relation among the elements of A , having the same number of places as P k .