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Topic: Axiomization of Number Theory
Replies: 52   Last Post: Aug 4, 2003 12:18 AM

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Charlie Johnson

Posts: 143
Registered: 12/10/04
Re: Axiomization of Number Theory
Posted: Jul 25, 2003 5:49 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply


It is axiomatized! It follows from the field axioms.

Lurch

"Charlie-Boo" <chvol@aol.com> wrote in message
news://3df1e59f.0307250955.79ee3a83@posting.google.com...
> Hello all,
>
> I am interested in axiomizing Number Theory. I'm not talking about
> some bogus list of properties of addition and multiplication, but
> rather a set of formal axioms and rules of inference that allows us (a
> program) to derive theorems from Number Theory.
>
> It seems to be a natural branch of mathematics to axiomize, since it
> figures so heavily in proofs concerning Logic (e.g. Godel's
> Incompleteness Theorems) and Logic is so easily axiomized. I have
> axiomized the Theory of Computation (a.k.a. Computability) and Program
> Synthesis of Number Theoretic functions (prime listing or checking,
> factoring, etc.) in

http://www.mathpreprints.com/math/Preprint/CharlieVolkstorf/20021008.1/1
> and http://www.arxiv.org/html/cs.lo/0003071 .
>
> The first step is to gather together a few dozen of the very simplest
> theorems from Number Theory. Then we look for primitives etc.
>
> The effort can be done here, or in private collaboration with me
> (contact me at the email address below) and whoever else is
> interested, with periodic progress reports posted here, culminating
> with a published paper.
>
> Charlie Volkstorf
> Cambridge, MA
> axiomize at aol dot com




Date Subject Author
7/25/03
Read Axiomization of Number Theory
Charlie-Boo
7/25/03
Read Re: Axiomization of Number Theory
Charlie Johnson
7/25/03
Read Re: Axiomization of Number Theory
Arief
7/25/03
Read Re: Axiomization of Number Theory
Jeffrey Ketland
7/28/03
Read Re: Axiomization of Number Theory
Charlie-Boo
7/28/03
Read Re: Axiomization of Number Theory
William Elliot
7/28/03
Read Re: Axiomization of Number Theory
Charlie-Boo
7/28/03
Read Re: Axiomization of Number Theory
Andrew Boucher
7/29/03
Read Re: Axiomization of Number Theory
Andrew Boucher
7/29/03
Read Re: Axiomization of Number Theory
Andrew Boucher
8/4/03
Read Re: Axiomization of Number Theory
Charlie-Boo
7/29/03
Read Re: Axiomization of Number Theory
Pete Moore
7/29/03
Read Re: Axiomization of Number Theory
Robin Chapman
7/29/03
Read Re: Axiomization of Number Theory
David C. Ullrich
7/29/03
Read Re: Axiomization of Number Theory
Robin Chapman
7/29/03
Read Re: Axiomization of Number Theory
David C. Ullrich
7/29/03
Read Re: Axiomization of Number Theory
Robin Chapman
7/30/03
Read Re: Axiomization of Number Theory
David C. Ullrich
7/30/03
Read Re: Axiomization of Number Theory
Robin Chapman
7/30/03
Read Re: Axiomization of Number Theory
David C. Ullrich
7/31/03
Read Re: Axiomization of Number Theory
Robin Chapman
7/29/03
Read Re: Axiomization of Number Theory
George Cox
7/29/03
Read Re: Axiomization of Number Theory
Per Eriksson
7/30/03
Read Re: Axiomization of Number Theory
Charlie-Boo
7/30/03
Read Re: Axiomization of Number Theory
Per Eriksson
7/31/03
Read Re: Axiomization of Number Theory
Robin Chapman
7/30/03
Read Re: Axiomization of Number Theory
David C. Ullrich
7/30/03
Read Re: Axiomization of Number Theory
Per Eriksson
7/30/03
Read Re: Axiomization of Number Theory
Mike Oliver
7/31/03
Read Re: Axiomization of Number Theory
David C. Ullrich
7/31/03
Read Re: Axiomization of Number Theory
Charlie-Boo
7/31/03
Read Re: Axiomization of Number Theory
tchow@lsa.umich.edu
7/31/03
Read Re: Axiomization of Number Theory
Per Eriksson
7/29/03
Read Re: Axiomization of Number Theory
Arief
7/30/03
Read Re: Axiomization of Number Theory
Keith Ramsay
7/30/03
Read Re: Axiomization of Number Theory
David C. Ullrich
7/30/03
Read Re: Axiomization of Number Theory
Andrew Boucher
7/30/03
Read Re: Axiomization of Number Theory
David C. Ullrich
7/30/03
Read Re: Axiomization of Number Theory
Andrew Boucher
7/30/03
Read Re: Axiomization of Number Theory
Mike Oliver
7/31/03
Read Re: Axiomization of Number Theory
Andrew Boucher
7/31/03
Read Re: Axiomization of Number Theory
Mike Oliver
7/31/03
Read Re: Axiomization of Number Theory
Aatu Koskensilta
7/31/03
Read Re: Axiomization of Number Theory
Andrew Boucher
7/31/03
Read Re: Axiomization of Number Theory
Mike Oliver
7/31/03
Read Re: Axiomization of Number Theory
Andrew Boucher
7/31/03
Read Re: Axiomization of Number Theory
Mike Oliver
7/31/03
Read Re: Axiomization of Number Theory
Andrew Boucher
7/31/03
Read Re: Axiomization of Number Theory
Mike Oliver
7/31/03
Read Re: Axiomization of Number Theory
Aatu Koskensilta
7/31/03
Read Re: Axiomization of Number Theory
Andrew Boucher
7/31/03
Read Re: Axiomization of Number Theory
Keith Ramsay
7/31/03
Read Re: Axiomization of Number Theory
Andrew Boucher

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