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Topic: Interpreting ZFC
Replies: 14   Last Post: Apr 30, 2013 3:45 PM

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Zaljohar@gmail.com

Posts: 2,665
Registered: 6/29/07
Re: Interpreting ZFC
Posted: Apr 30, 2013 3:45 PM
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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 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!





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