FOM: Nonstandard models of N
Todd Wilson
twilson at csufresno.edu
Fri Mar 9 20:45:33 EST 2001
Dear FOMers:
As we know, every countable non-standard model of arithmetic has order
type
NN = omega + (Z * Q) ,
where Z and Q are the order types of the integers and rationals, and
where the successor function s : NN -> NN is obvious. Are there any
explicit definitions of + and * on NN that make (NN, 0, s, +, *) into
a model of arithmetic? If not, is there a proof that such definitions
are impossible (for example, a model of set theory in which all models
of arithmetic are standard)? In either case, where was this first
established? Thanks,
--
Todd Wilson A smile is not an individual
Computer Science Department product; it is a co-product.
California State University, Fresno -- Thich Nhat Hanh
More information about the FOM
mailing list