Definition:Morse-Kelley Set Theory
Morse-Kelley set theory is a system of axiomatic set theory.
It is a stronger form of Zermelo-Fraenkel-Skolem set theory which allows not only for first order formulas to specify the existence of properties of sets, but also defines properties by quantifying over properties as well as over sets.
Source of Name
This was proven by Gödel's Incompleteness Theorems.
- 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $1$: General Background: $\S 9$ Zermelo set theory