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

(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).

**References**

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.

© 1996-9

1999-05-26