Let
be an
formula, where
and
is the language of ordered rings . Then there exist and such that
is equivalent to

(Marker 1996, Wilkie 1996). In other words, every formula is equivalent to an existential formula and every definable set is the projection of an exponential variety (Marker 1996).

Marker, D. "Model Theory and Exponentiation." Not. Amer. Math. Soc.43, 753-759, 1996.Wilkie, A. J.
"Model Completeness Results for Expansions of the Ordered Field of Real Numbers
by Restricted Pfaffian Functions and the Exponential Function." J. Amer.
Math. Soc.9, 1051-1094, 1996.