[FOM] Short or very short Gôdel codes, anyone?
rgheck at brown.edu
Mon Jul 9 14:35:00 EDT 2012
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
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