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This is my question, I do not have found any paper or book explaining this but this is repeated a lot. So why is V a proper class in this set theory?

Andrés E. Caicedo
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Rodrigo Tavares
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  • Can you provide an example of where you see $V$ being used? – benguin Aug 28 '16 at 16:21
  • Its used in NF and NFU set theories because in there it is a set. My goal is study all theories with universal set. because of large sets, like he set of all groups, Frege cardinal numbers, and categories. But in NF the category of sets is not cartesian closed wich makes NF loose its value. – Rodrigo Tavares Aug 28 '16 at 16:25
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    According to Wikipedia, anyway, $x=x$ is a positive formula. So $V={x\mid x=x}$ is a set. Unless by $V$ you don't mean the collection of all sets. – Asaf Karagila Aug 28 '16 at 16:44
  • Ah, sorry I confused "proper set" with "proper class". Beacause "proper class" has standart usage, but "proper set" not. I think this wiki article should be improved. – Rodrigo Tavares Aug 28 '16 at 16:49

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