Date: Aug 19, 2013 1:20 AM
Author: Graham Cooper
Subject: Re: set builder notation
On Sunday, August 18, 2013 6:21:12 PM UTC-7, Seymour J. Shmuel Metz wrote:

> at 11:30 AM, dullrich@sprynet.com said:

>

> >(2) {x | x in A and P(x)}.

>

>

>

> >No:

>

>

>

> >No, because (2) is actually not a "legal"

>

> >construction of a set!

>

>

>

> It may not be legal in ZF, but it's perfectly legal in, e.g., NF. Of

>

S = { x | xeZ & p(x) }

Obviously this is going to create a hierarchy of subsets..

that cannot directly form contradictions... ala ZFC

A much simpler resolution to Russell's Set is to declare consistency.

[THEOREM 1]

ALL(T):THEOREMS T

The Theory needs some declaration to distinguish FALSE WFF from TRUE WFF.

Using Set Specification with p(X)<->X~eX

just results in a FALSE WFF.. a failed specification attempt.

EXIST(SET)ALL(X) XeSET<->p(X) -->[T|F]

Just demote SET SPECIFICATION to a WFF not a theorem.

Herc

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