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Topic: set builder notation
Replies: 12   Last Post: Aug 24, 2013 1:38 AM

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Graham Cooper

Posts: 4,495
Registered: 5/20/10
Re: set builder notation
Posted: Aug 19, 2013 1:20 AM
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On Sunday, August 18, 2013 6:21:12 PM UTC-7, Seymour J. Shmuel Metz wrote:
> at 11:30 AM, 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.


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.


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