As I understand the ZFC solution to Russell's paradox, since {x|x[itex]\notin[/itex]x} must be {x|x[itex]\notin[/itex]x}[itex]\cap[/itex]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[itex]\notin[/itex]x}[itex]\cap[/itex]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.(adsbygoogle = window.adsbygoogle || []).push({});

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

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