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

```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 ?

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```

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