Morse-Kelley set theory

The **Morse–Kelley set theory** ($MK$) is an axiomatic approach to 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*.

Revised on January 8, 2011 05:10:19
by Toby Bartels
(98.19.48.164)