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Re: Goedel Numbers

  • To: mathgroup at
  • Subject: [mg64197] Re: [mg64175] Goedel Numbers
  • From: Bob Hanlon <hanlonr at>
  • Date: Sun, 5 Feb 2006 04:44:51 -0500 (EST)
  • Reply-to: hanlonr at
  • Sender: owner-wri-mathgroup at








Bob Hanlon

> From: "Brambilla Roberto Luigi (CESIRICERCA)" <RLBRAMBILLA at>
To: mathgroup at
> Subject: [mg64197] [mg64175] Goedel Numbers
> 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, 
> 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 ?
> CESI SpA ha adottato il Modello Organizzativo ai sensi del D.Lgs.231/2001, 
in forza del quale l'assunzione di obbligazioni da parte della Società avviene 
con firma di un procuratore, munito di idonei poteri.
> CESI adopts a Compliance Programme under the Italian Law (D.Lgs.
231/2001). According to this CESI Compliance Programme, any commitment 
of CESI is taken by the signature of one Representative granted by a proper 
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