[FOM] Short or very short Gôdel codes, anyone?

[Frode Bjørdal]

2012/7/10 jean paul van bendegem <jpvbende at vub.ac.be>

> **
> One of the shortest codes I am aware of is to be found in "Computability
> and Logic" (5th edition) by Boolos, Burgess and Jeffrey, page 188. It
> groups together symbols by a code consisting of an initial digit smaller
> than 9 and then adding 9's. Take, e.g., a list of variables: v1, v2, v3,
> .... These will be coded into,say, 5, 59, 599, ..., so vn requires n signs
> in the code, satisfying your requirement. The codes of the individual signs
> are simply joined by concatenation. Jean Paul
>

I do not see that this set up satifies the requirements for being very
short codes. Are initial 0's allowed

Frode


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> ----- Original Message -----
> *From:* Frode Bjørdal <frode.bjordal at ifikk.uio.no>
> *To:* Foundations of Mathematics <fom at cs.nyu.edu>
> *Sent:* Monday, July 09, 2012 4:14 AM
> *Subject:* [FOM] Short or very short Gôdel codes, anyone?
>
>  Has someone used short or very short Gôdel codings to arithmesize
> syntax? If so, who, where and how? A very short Gôdel coding would in my
> idiolect be one where an expression with n symbols, in a system with an
> alphabet of m symbols, would have a Gôdel number smaller than m raised to n.
>
>
> Frode Bjørdal
> Professor i filosofi
> IFIKK, Universitetet i Oslowww.hf.uio.no/ifikk/personer/vit/fbjordal/index.html
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-- 


Frode Bjørdal
Professor i filosofi
IFIKK, Universitetet i Oslowww.hf.uio.no/ifikk/personer/vit/fbjordal/index.html
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