```Date: Apr 30, 2013 3:45 PM
Author: Zaljohar@gmail.com
Subject: Re: Interpreting ZFC

On Apr 29, 5:36 am, Graham Cooper <grahamcoop...@gmail.com> wrote:> On Apr 28, 3:58 am, Zuhair <zaljo...@gmail.com> wrote:>>>>>>>>>> > On Apr 27, 3:55 pm, Jan Burse <janbu...@fastmail.fm> wrote:> > > No>> > > Zuhair schrieb:>> > > > Pre-ZFC is a first order theory with the following axioms:>> > > > (1) Powerful Boundedness: if phi is a formula in which x,y are free,> > > > then> > > > all closures of:>> > > > EB: (Vy in B(Ex C A:phi)) & (Vx C A ((Ey:phi) ->(Ey in B:phi)))>> > > > are axioms.>> > > > C is subset relation.> > > > V;E signifies universal; existential quantification respectively.>> > > > 2) Infinity.>> > > > />> > > > The whole of ZFC can be interpreted in Pre-ZFC.>> > > > Zuhair>> > Hmmm,... you must have figured out some flaw somewhere, what is it?>> > Zuhair>> B is any set in the world of mathematics!>> EB: (Vy in B(Ex C A:phi)) & (Vx C A ((Ey:phi) ->(Ey in B:phi)))>> is>> Exist B   ALL y in B ... Exist X C A:phi> &> All X C A  (Exist y:phi  ->  Exist y in B:phi )>> ***************>> 1st line:>> yeB  <->  SUBSET X OF A with elements that satisfy phi>> 3rd line:>> ALL subsets of A..> y satisfies phi -> y e B (that satisfy phi)>> --------------->> firstly, is the final phi in B:phi necessaryYes.> since phi already designates members of B>yea but it doesn't enforce which of phi objects are members of B.The last phi is necessary to enforce one phi object for Eeach x subsetof A, to be a member of B.> secondly,  All subsets of A is a POWERSET operation> on all SETS in the THEORY which has huge complexity>> thirdly, this is starting to look like mereology where> on starting equation is given to derive the rest..>> the problem with mereology is it uses ALL(S) quantifier> and C (subset) to co-define each other..>> fourth, perhaps you could show LINE BY LINE how> phi(x) <-> x ~e x>> is barred from inferring an existent set B.>> Herc> --> EARTH, WIND, FIRE, WATER...  is my bet!
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