Wilkie's Theorem
Let 
be an 
formula, where 
and 
is the language of ordered rings 
. Then there are 
and
such that isequivalent to
(Wilkie 1996). In other words, every formula is equivalent to an existential formula and every definable set is theprojection 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.
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