Some remarks on Schanuel's conjecture

Schanuel's Conjecture is the statement: if x(1),...,x(n) is an element of C are linearly independent over Q, then the transcendence degree of Q(x(1),...,x(n), exp(x(1)),...,exp(x(n))) over Q is at least n. Here we prove that this is true if instead we take infinitesimal elements from any ultrapower of C, and in fact from any nonarchimedean model of the theory of the expansion of the field of real numbers by restricted analytic functions. (C) 2001 Elsevier Science B.V. All rights reserved.