David Hartley wrote: > In message <52236CD3.email@example.com>, Jim Burns <firstname.lastname@example.org> 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.
-- Sorrow in all lands, and grievous omens. Great anger in the dragon of the hills, And silent now the earth's green oracles That will not speak again of innocence. David Sutton -- Geomancies