
Re: set builder notation
Posted:
Aug 19, 2013 1:20 AM


On Sunday, August 18, 2013 6:21:12 PM UTC7, 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) >[TF]
Just demote SET SPECIFICATION to a WFF not a theorem.
Herc  www.phpPROLOG.com

