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Topic: Using classes instead of sets
Replies: 26   Last Post: Apr 1, 2013 8:04 PM

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Frederick Williams

Posts: 2,166
Registered: 10/4/10
Re: Using classes instead of sets
Posted: Mar 28, 2013 3:27 PM
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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 Russell-type 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



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