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# Def/Class

Definition of Class: Classes are used to make rigorous the idea of "collections of sets", which themselves may be "too big" to be a set. Rather than introducing classes axiomatically (as in Bernays-Godel set theory), we follow Devlin in using classes as abbreviations for expressions involving unary predicates.

Formally, a class is simply a unary predicate. However, if $\Phi(x)$ is a unary predicate, we speak of the "class of sets $x$ satisfying $\Phi(x)$", written (perhaps too) suggestively as $\{ x \vert \Phi(x) \}$, or $\{ x \mbox{ such that } \Phi(x) \}$.

## Logical Connections

This definition logically relies on the following definitions and statements: Def/Unary predicate, Def/Russell predicate

The following statements and definitions logically rely on the material of this page: Def/Multiplication of cardinal numbers

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