In article <firstname.lastname@example.org>, Peter Percival <email@example.com> wrote:
> David Hartley wrote: > > In message <52236CD3.firstname.lastname@example.org>, Jim Burns <email@example.com> writes > >> If I say that I have a set with a semi-infinite, > >> discrete, linear order, (N, <), is that enough to > >> define the naturals? > > > > I'm afraid not. Thee are many other orderings satisfying your axioms. > > E.g. N + Z - i.e. a copy of N followed by a copy of Z. > > Also, there is no recursive set of first order axioms that will capture > just the natural numbers.