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

 Messages: [ Previous | Next ]
 fom Posts: 1,968 Registered: 12/4/12
Re: Prime Interger Topology
Posted: Oct 21, 2013 7:52 AM

On 10/21/2013 3:24 AM, William Elliot wrote:
> 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
>

Oh! The pairing function could.

I meant the codings on the relations in the theory.

Given a definite model, those relations would be given
definite values. Applying the coding to the relations
would map each relation back into the natural numbers.

It is the set of such relations to which I refer.

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