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
- Thread-index: AcYoqTkT9Zn4P9JDRmyQtg7rLQyILw==
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 ?
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