From: utzoo!decvax!harpo!npoiv!npois!houxm!5941ux!machaids!hocda!spanky!ka
Newsgroups: net.math
Title: Re: I am trying to comprehend [set theory]
Article-I.D.: spanky.194
Posted: Mon Feb  7 22:00:54 1983
Received: Wed Feb  9 05:21:53 1983
References: ihuxr.321

To answer the second question first, I have never seen the notation
"E !y", but I assume from the context that the author means "there
exists exactly one y."

I intermingled the formal and English proofs of the nonexistence
of the set of all set in the hopes that each version would clarify
the other:

Proof is by contradiction.  Assume that the set of all sets exists.
1)	Ax x z z z ~(z ~(y x < z ^ phi) where phi is a formula NOT INVOLVING y.
The difference is that in (2a), the restriction on phi is written in
English, while in (2) the restriction is enforced by allowing only the
property "p", rather than the entire formula "phi", to vary.

I think Lew's confusion stems from a misunderstanding of this re-
striction.  In (2a), phi should not depend on y; but that doesn't
prevent us from later substituting y for x, as I do in (6).  The
reason I prefer (2) to (2a) is that the restriction is implicit
in to formula, which avoids such confusion.
				Kenneth Almquist