# Contents

## Idea

The Morse-Kelley set theory or Morse-Kelley class theory ($MK$) is an axiomatic approach to class theory and set theory which has both classes and sets. Whereas NBG (which also has both classes and sets) is conservative? over ZFC, Morse–Kelley is not a conservative extension of $NBG$. The principal difference from $NBG$ is that $MK$ allows arbitrary formulas $\phi$ appearing in the class comprehension axiom schema (in particular, formulae with quantifiers ranging over classes themselves).

The approach is explained in the appendix to John Kelley‘s 1955 book General Topology.