Re: Resolving the paradoxes of set theory

From: Josh Purinton (usenet-noreply.a.jp_at_xoxy.net)
Date: 10/31/04 

Date: 31 Oct 2004 20:38:42 GMT

In article <992b156f.0410310547.74822ce7@posting.google.com>,
George Greene <greeneg@cs.unc.edu> wrote:
>In ZFC, that's not even possible. In ZFC, EVERYthing is a set.

This does not prevent us from speaking rigorously of classes; in the
standard metatheory of ZFC, a class is just a formula, possibly with
free variables.

As Keith Ramsay wrote recently in sci.math: "One useful trick is to
realize that when we're working with proper classes, we're really
dealing with the predicates that define them. So with V, really we're
working with the predicate that's always true, like 0=0."

>Idiot, the mere fact that you put { }'s around it
>MEANS THAT YOU ARE CALLING IT A *SET*, as well as a class.

Again, not true.

"A general specifiable collection, which may or may not be a set, will be
called a class. A class is given by a formula phi(x) as the class of all
objects x for which phi(x) holds. Such a class will be denoted by {x |
phi(x)}." (Azriel, _ Basic Set Theory _ , p 9.)

"All the theorems in this book will be proved in ZF or ZFC." (ibid., p 24.) 

-- 
Josh Purinton

Relevant Pages

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