Abstract

As is well known, some paradoxes arise through inadequate analysis of the meanings of terms in a language, an adequate analysis showing that the paradoxes arise through a lack of separation of an object theory and a metatheory. Under such an adequate analysis in which parts of the metatheory are modelled in the object theory, the paradoxes give way to remarkable theorems establishing limitations of the object theory.Such a modelling is often accomplished by a Gödel numbering. Here we shall use a somewhat different technique in axiomatic set theory, from which we shall reap a few results having the effect of comparing the strength of various axiom schema of comprehension for sets and classes. Similar results were obtained by A. Mostowski [7] using Gödel numbering.