Theories of Rules, Sets, and Classes

Abstract

In this chapter we will discuss Feferman’s theories of rules and classes, and some variants of them invented by the author. These theories are based on the theory EON described in Chap. VI. We add to EON a unary predicate S(x) to denote, as in IZF, “x is a set”. This does not mean, however, that we have the same notion of “set” in mind as when formulating IZF. Feferman deliberately used the words “classification” or “class” instead; the difference between “class” and “set” will be discussed below. Given the formal set-up just described, the question that has to be answered is

• What are appropriate set-existence axioms?