# nLab 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)