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:

>

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> > 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 necessary

Yes.

> 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 subset

of 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!