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)
• Sender: owner-wri-mathgroup at wolfram.com

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

code=Range[Length[alphabet]];

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+*=**Â¬**\$""
> 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 SocietÃ  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.
>
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>

```

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