
Re: Using classes instead of sets
Posted:
Mar 28, 2013 3:27 PM


pepstein5@gmail.com wrote: > > [...] Classes are allowed to contain other classes after all.
If X, Y are proper classes in NBG, one may not have X in Y, but one may have X subset Y. So it depend on what 'contains' means.
> Of course, we get Russelltype paradoxes if we allow entities to contain themselves, whether the entities be sets or classes.
So by 'contain' you mean $\in$ I suppose. But the language of set theory allows x \in x as a formula, but it doesn't allow {x  x in x} as a set. Otoh, {x in y  x in x} is a set if y is.
[I know nothing about set theories that aren't ZF or NBG, and I know next to nothing about those.]
 When a true genius appears in the world, you may know him by this sign, that the dunces are all in confederacy against him. Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting

