fom
Posts:
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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. > > https://groups.google.com/forum/m/#!topic/sci.logic/dFKEENfh6w > Apoorv >
If I am reading your notation correctly,
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.

