# Morse-Kelley Class Comprehension axiom and Russell's paradox

1. Dec 27, 2013

As I understand the ZFC solution to Russell's paradox, since {x|x$\notin$x} must be {x|x$\notin$x}$\cap$S for some set S, the paradox goes away, but in Morse-Kelley, if I understand Class Comprehension correctly, although again there must be some M such that {x|x$\notin$x}$\cap$M, this M may be a proper class, which no longer is as limiting as the ZFC version, and hence no longer gives the same solution. So either I am going wrong somewhere, or MK solves Russell's Paradox in a different way. I would be grateful for enlightenment. Thanks.