On Prucnal's Model-determinated Logic and Definable Predicates

Let L be a first-order language and let M = 〈M, I〉 be a model for L. Then every formula φ(x1, . . . , xn) of L determines a unique n-place predicate: φ = {〈a1, . . . , an〉 ∈M n : M |= φ[a1, . . . , an]} Here, of course, the notation φ(x1, . . . , xn) is used to indicate that the free variables of φ constitute a subset of {x1, . . . , xn} (see [1] p. 24). A n-placed relation R ⊆M is said to be definable in M if there exists a formula φ(x1, . . . , xn) in L such that R = φ . Received February 15, 200