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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 22, 2013 6:52 PM
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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/dFK-EENfh6w
>>
>>> -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?





Date Subject Author
7/10/13
Read Re: Ordinals describable by a finite string of symbols
Aatu Koskensilta
7/10/13
Read Re: Ordinals describable by a finite string of symbols
David C. Ullrich
7/10/13
Read Re: Ordinals describable by a finite string of symbols
Sandy
7/10/13
Read Re: Ordinals describable by a finite string of symbols
fom
7/12/13
Read Re: Ordinals describable by a finite string of symbols
apoorv
7/15/13
Read Re: Ordinals describable by a finite string of symbols
fom
7/16/13
Read Re: Ordinals describable by a finite string of symbols
Shmuel (Seymour J.) Metz
7/19/13
Read Re: Ordinals describable by a finite string of symbols
apoorv
7/19/13
Read Re: Ordinals describable by a finite string of symbols
fom
7/20/13
Read Re: Ordinals describable by a finite string of symbols
apoorv
7/20/13
Read Re: Ordinals describable by a finite string of symbols
Peter Percival
7/20/13
Read Re: Ordinals describable by a finite string of symbols
apoorv
7/21/13
Read Re: Ordinals describable by a finite string of symbols
apoorv
7/21/13
Read Re: Ordinals describable by a finite string of symbols
apoorv
7/21/13
Read Re: Ordinals describable by a finite string of symbols
fom
7/22/13
Read Re: Ordinals describable by a finite string of symbols
apoorv
7/22/13
Read Re: Ordinals describable by a finite string of symbols
fom
7/23/13
Read Re: Ordinals describable by a finite string of symbols
apoorv
7/23/13
Read Re: Ordinals describable by a finite string of symbols
apoorv
7/24/13
Read Re: Ordinals describable by a finite string of symbols
apoorv
7/27/13
Read Re: Ordinals describable by a finite string of symbols
apoorv
7/27/13
Read Re: Ordinals describable by a finite string of symbols
fom
7/10/13
Read Re: Ordinals describable by a finite string of symbols
Aatu Koskensilta

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