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

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 fom Posts: 1,968 Registered: 12/4/12
Re: Ordinals describable by a finite string of symbols
Posted: Jul 21, 2013 3:53 PM

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))
g(3)= g(f(3,w))

which would seem to violate the idea that
the Goedel numbering corresponds with a
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