Some new results in definability
Chen Chung Chang · Bulletin of the American Mathematical Society · 1964
Consider a first-order language <£ with identity and unitary predicate symbols.We let the letter A range over the models for <£.Let P, Q be new unary predicate symbols and let <£(P, Q) be the new first-order language with the additional predicates P and Q. Models for £(P, Q) will be written as (A, P, Q) where P and Q are subsets of A. Let T and S be sets of sentences of £(P, Q) (or of <£(P), or <£).We write T\-S to mean that every model of T is a model of 5. | X\ shall denote the cardinal of the set X.The following two known results are due to Beth [l ] and Svenonius