Ordinal Definable Sets

Abstract

Let Φ(x) be a monadic expression whose parameters are all in some set X; the value of this expression in X is then a subset of ^{x}X. By the canonical bijection of ^{x}X on to X (that which sends {<x, u>} to u, for every u∈X) there corresponds to this subset a subset of X itself, written val (Φ, X), and also called, by a slight abuse of language, the value of Φ in X.