An interpretation of star free expressions over the reals is provided. The
expressive power of star free expressions is compared to the expressive pow
er of monadic first-order logic of order over the reals. It is proved that
these formalisms have the same expressive power. This result provides a gen
eralization of the classical McNaughton-Papert theorem (1971) from the fini
te orders to the order of the reals. (C) 2000 Elsevier Science B.V. All rig
hts reserved.