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Goedel Numbers

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

I'm trying to build Goedel numbers by means of Mathematica using the following idea:
any string can use only the following 16 characters 
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.


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





Given this, then 


and the Goedel number is simply given by 


Thank you all ! 

PS.:  I can use 
aa=To characterCode[alphabet]
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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