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

[Richard Heck]

On 07/08/2012 10:14 PM, Frode Bjørdal wrote:
> 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.
>
So-called "efficient codings" do get used when working in very weak 
systems of arithmetic, meaning: systems that do not have exponentiation. 
I don't think they go quite as far as you're suggesting, but I've not 
checked the details by any means. See section V.3 in Hajek and Pudlak's 
book.

Richard Heck