  This article presents two constructions motivated by a conjecture of L. van
den Dries and C. Miller concerning the restricted analytic field with
exponentiation. The first construction provides an example of two o-minimal
expansions of a real closed field that possess the same field of germs at
infinity of one-variable functions and yet define different global one-variable
functions. The second construction gives an example of a family of infinitely
many distinct polynomially bounded reducts (all this in the sense of
definability) of the restricted analytic field with exponentiation.
