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Topic: ZFC = only PA (a glorified adding machine) and some arbitrary
statements about sets

Replies: 5   Last Post: Jun 9, 2013 5:04 AM

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Charlie-Boo

Posts: 1,588
Registered: 2/27/06
Re: ZFC = only PA (a glorified adding machine) and some arbitrary
statements about sets

Posted: Jun 9, 2013 5:04 AM
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On Jun 8, 4:37 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
> On Jun 9, 1:07 am, Peter Percival <peterxperci...@hotmail.com> wrote:
>

> > Charlie-Boo wrote:
> > > On Jun 7, 2:24 am, Zeit Geist <tucsond...@me.com> wrote:
>
> > >> It was actually a desire to assure the consistency of the Calculus
> > >> that eventually lead to the creation of ZFC.

>
> > > You mean avoid Russell's Paradox?
>
> Just use ALL(F):WFF  F<->F
>
> E(S)A(X) XeS<->X~eX
> <->
> E(S)A(X) XeS<->X~eX
>
> E(S)A(X) XeS<->X~eX
> <->
> E(S)E(S) SeS<->S~eS
>
> E(S)A(X) XeS<->X~eX
> <->
> FALSE
>
> CONTRADICTION CONTAINED IN A SUB-FORMULA!
>
> ~EXIST(RUSSELSET)
>
> THAT SIMPLE!
>
>
>

> > Zermelo created his set theory in order to prove that every set could we
> > well-ordered.

>
> PROOF:   0;.44444444544444454444444454454444444544444...
>
> Herc


Very good - for starters. Now list as many theorems as you can that
use the same proof but with different constants, in this case, instead
of set and membership. Then identify a theorem that is proven with
just one additional step beyond one of these, and apply it to the rest
of the theorems. Here's a first step: The set of Turing Machines that
do not halt yes on themselves is not recursively enumerable.

C-B



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