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MathGroup Archive 2006

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Goedel Numbers

  • To: mathgroup at smc.vnet.net
  • Subject: [mg64175] Goedel Numbers
  • From: "Brambilla Roberto Luigi (CESIRICERCA)" <RLBRAMBILLA at cesi.it>
  • Date: Sat, 4 Feb 2006 04:13:29 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com
  • Thread-index: AcYoqTkT9Zn4P9JDRmyQtg7rLQyILw==

Hi,
I'm trying to build Goedel numbers by means of Mathematica using the following idea:
any string can use only the following 16 characters 
alphabet="()x'0S+*=**¬**$""
If you can't read it, it is the 
i.e. :   open bracket, close bracket, X, ', 0 ,S ,+ ,* ,= ,And, Or, Not ,RightArrow, LeftRightArrow, Exists, ForAll

and the corrisponding coding number are given by an arbitrary number list, es.

code={1,2,3...,16}

I need a quick way to get the list of code numbers of a given formula

(*example*) 

p="SS0*X=(X*X)+S0"

gg=GoedelNumber[p]

{6,6,5,8,3,9,1,3,8,3,2,7,6,0}

Given this, then 

ee=Table[Prime[j],{j,1Length[gg]];

and the Goedel number is simply given by 

G=ee^gg


Thank you all ! 
Roberto

PS.:  I can use 
aa=To characterCode[alphabet]
{40,41,88,39,48,83,43,42,61,8743,8744,172,8594,8596,8707,8704}
pp=ToCharacterCode[p]
{83,83,48,42,88,61,40,88,42,88,41,43,83,48}
but these are too unuseful large numbers for exponentiaion.
How can I substiture in pp list : 40 with1, 41 with2, 88 with3  ...8704 with16 ?









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