
Re: Using classes instead of sets
Posted:
Mar 30, 2013 4:26 PM


On 20130329, Shmuel Metz <spamtrap@library.lspace.org.invalid> wrote: > In <f8ral8lndkanp4gd70pu1fmblq4g912o74@4ax.com>, on 03/29/2013 > at 06:07 AM, quasi <quasi@null.set> said:
>>There are certain concepts for which sets are inadequate and classes >>come to the rescue. For example, we need the class concept if we >>want to define an equivalence on the collection of all groups, since >>that collection is not a set.
> There's no such set in ZFC, but there are set theories in which it > exists aqnd is a set.
I do not see how that can be the case, excluding Quine's _New Foundations_, which has lots of its problems.
There must be as many groups equivalent to a given group as there are sets, as {<x,y>: y \in g} for a given group g has an obvious operation which makes the class of elements a group isomorphic to g. This even holds if the group is a proper class. So the collection of all groups is at least as large as the collection of all sets.
 This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)4946054 FAX: (765)4940558

