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Topic: Peano's Integers Modulus n.
Replies: 12   Last Post: Mar 23, 2014 4:44 AM

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LudovicoVan

Posts: 3,201
From: London
Registered: 2/8/08
Re: Peano's Integers Modulus n.
Posted: Mar 23, 2014 4:44 AM
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"William Elliot" <marsh@panix.com> wrote in message
news:Pine.NEB.4.64.1403230103450.18075@panix2.panix.com...

> What is there to explain? You showed omega_0 + 1 isn't a model,
> Are you wanting to tinker with it so it could be?


I did ask few questions, the main ones being:

About proving that the integers modulus z+1 are a model for your axioms, it
seems trivial to check that all axioms hold (using the usual successor
function for the integers modulo z+1 as S), except for the induction axiom:
how does one prove that they satisfy your induction axiom? Indeed, more
generally, though the question may be misguided, I wonder: to prove that
some structure is a model for some axioms, which theory is one
supposed/allowed to use?

Julio





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