Date: Mar 30, 2013 4:26 PM
Author: Guest
Subject: Re: Using classes instead of sets

On 2013-03-29, 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 groupas there are sets, as {<x,y>: y \in g} for a given group ghas an obvious operation which makes the class of elementsa group isomorphic to g.  This even holds if the group is a proper class.  So the collection of all groups is at leastas large as the collection of all sets.-- This address is for information only.  I do not claim that these viewsare those of the Statistics Department or of Purdue University.Herman Rubin, Department of Statistics, Purdue Universityhrubin@stat.purdue.edu         Phone: (765)494-6054   FAX: (765)494-0558