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Topic: Ordinals describable by a finite string of symbols
Replies: 24   Last Post: Jul 27, 2013 12:38 PM

 Messages: [ Previous | Next ]
 apoorv Posts: 53 Registered: 4/11/13
Re: Ordinals describable by a finite string of symbols
Posted: Jul 22, 2013 4:33 PM

On Monday, July 22, 2013 1:23:53 AM UTC+5:30, fom wrote:
> On 7/21/2013 1:40 PM, apoorv wrote:
>

> > I needed some clarification on Godel Numbering . I had asked it earlier .
>
> > Maybe I have more luck this time.
>
> >
>
>
> > -Apoorv
>
> >
>
>
>
>
>
>
> g(x)= Goedel number of 'x'
>
>
>
> Actually, your notation confuses me (due
>
> to relative lack of recent experience).
>
>
>
> To stipulate something along the lines
>
> of
>
>
>
> g(1)=godel number of f(1,w)
>
> g(2)=godel number of f(2,w)
>
> g(3)=godel number of f(3,w) etc
>
>
>
>
>
> would seem to be
>
>
>
> g(1)= g(f(1,w))
>
> g(2)= g(f(2,w))
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> g(3)= g(f(3,w))
>
>
>
> which would seem to violate the idea that
>
> the Goedel numbering corresponds with a
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> unique naming of symbols.
>
>
>
> Now, if your countable language is indexed
>
> by the natural numbers and the argument to
>
> 'g' is the index of the given formula, then
>
> the numerals on the left have no relation
>
> to the numerals on the right. In that case,
>
> the correspondence of your listing would have
>
> to be thought as accidental.

Date Subject Author
7/10/13 Aatu Koskensilta
7/10/13 David C. Ullrich
7/10/13 Sandy
7/10/13 fom
7/12/13 apoorv
7/15/13 fom
7/16/13 Shmuel (Seymour J.) Metz
7/19/13 apoorv
7/19/13 fom
7/20/13 apoorv
7/20/13 Peter Percival
7/20/13 apoorv
7/21/13 apoorv
7/21/13 apoorv
7/21/13 fom
7/22/13 apoorv
7/22/13 fom
7/23/13 apoorv
7/23/13 apoorv
7/24/13 apoorv
7/27/13 apoorv
7/27/13 fom
7/10/13 Aatu Koskensilta