LudovicoVan
Posts:
4,025
From:
London
Registered:
2/8/08


Re: Peano's Integers Modulus n.
Posted:
Mar 23, 2014 1:19 AM


"William Elliot" <marsh@panix.com> wrote in message news:Pine.NEB.4.64.1403222106350.8893@panix1.panix.com... > On Sun, 23 Mar 2014, Julio Di Egidio wrote: >> "William Elliot" <marsh@panix.com> wrote in message > >> > > > Let N be a set and S:N > N an injection and 0 & z be two elements >> > > > of >> > > > N > >> > > > Assume Sz = 0 and the schemata, >> > > > if A subset N, 0 in A and for all n in A, Sn in A, >> > > > then A = N. >> > > > >> > > > Are the integers modulus z a model for these axioms? > >> There is an error in that a model would be the integers modulo z+1, not >> modulo >> z. Then 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: which makes me wonder, in which theory is one supposed/allowed to >> do >> the proof? > > No. Let N = { 0,1,2 } be the integers modulus 3. > Then z = 2 and Sz = 2 + 1 = 3 = 0.
No what?
No answer to the other questions?
Julio

