  In this paper we introduce the concept of O-asymptotic classes of finite
structures, melding ideas coming from 1-dimensional asymptotic classes and
o-minimality. The results we present here include a cell-decomposition result
for O-asymptotic classes and a classification of their infinite ultraproducts:
Every infinite ultraproduct of structures in an O-asymptotic class is superrosy
of U-thorn-rank 1, and NTP2 (in fact, inp-minimal).
