fom
Posts:
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Registered:
12/4/12


Re: Ordinals describable by a finite string of symbols
Posted:
Jul 22, 2013 6:52 PM


On 7/22/2013 3:33 PM, apoorv wrote: > 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. >
Did I miss a reply somewhere?

