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. > > > > > > 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.

