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Topic: Product, Filters and Quantales
Replies: 31   Last Post: Oct 21, 2013 7:52 AM

 Messages: [ Previous | Next ]
 William Elliot Posts: 2,637 Registered: 1/8/12
Re: Prime Interger Topology
Posted: Oct 21, 2013 4:24 AM

On Sun, 20 Oct 2013, fom wrote:
> On 10/20/2013 9:58 PM, William Elliot wrote:
> >
> > Why relations? Aren't functiosn used to manage the undue complexity of
> > relations?

>
> This is the pair coding function from Goedel's
> lemma in Kaye's "Models of Peano Arithemtic"
>
> < x, y > = [ ( x + y )( x + y + 1) / 2 ] + y
>
> Given any "definite" model of my axioms, I
> could collapse the relations into sets of
> numbers arithmetically.
>
> Those sets probably could not be represented recursively.

(0,0) = 0
(x+1, 0) = (x + 1)(x + 2)/2 = x(x + 1)/2 + x + 1 = (x,0) + x + 1

(x, y+1) = (x + y + 1)(x + y + 2)/2 + y + 1
= (x + y)(x + y + 1)/2 + x + y + 1 + y + 1
= (x,y) + x + y + 2

Date Subject Author
10/9/13 William Elliot
10/10/13 Victor Porton
10/11/13 William Elliot
10/11/13 Victor Porton
10/12/13 William Elliot
10/12/13 Victor Porton
10/12/13 William Elliot
10/14/13 Victor Porton
10/15/13 William Elliot
10/15/13 Victor Porton
10/16/13 William Elliot
10/16/13 Victor Porton
10/17/13 William Elliot
10/17/13 Victor Porton
10/17/13 William Elliot
10/18/13 Victor Porton
10/18/13 William Elliot
10/19/13 Victor Porton
10/19/13 William Elliot
10/19/13 William Elliot
10/20/13 fom
10/20/13 William Elliot
10/20/13 fom
10/20/13 William Elliot
10/20/13 William Elliot
10/20/13 fom
10/20/13 William Elliot
10/20/13 fom
10/21/13 fom
10/21/13 William Elliot
10/21/13 fom
10/20/13 William Elliot