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MathGroup Archive 2006

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Re: Goedel Numbers

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

alphabet=Characters["()X'0S+*=??¬????"];

code=Range[Length[alphabet]];

repl=Thread[alphabet->code];

GoedelNumber[p_String]:=Characters[p]/.repl;

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

gg=GoedelNumber[p]

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


Bob Hanlon

> 
> From: "Brambilla Roberto Luigi (CESIRICERCA)" <RLBRAMBILLA at cesi.it>
To: mathgroup at smc.vnet.net
> 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, 
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 ?
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 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 
Power of Attorney.
> 
> Le informazioni contenute in questo messaggio di posta elettronica sono 
riservate e confidenziali e ne e' vietata la diffusione in qualsiasi modo o 
forma. Qualora Lei non fosse la persona destinataria del presente messaggio,   
La invitiamo a non diffonderlo e ad eliminarlo, dandone gentilmente 
comunicazione al mittente.
> The information included in this e-mail and any attachments are 
confidential and may also be privileged. If you are not the correct recipient, 
you are kindly requested to notify the sender immediately, to cancel it and 
not to disclose the contents to any other person.
> 
> 


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