An effective version of Wilkie's theorem of the complement and some effective o-minimality results

@article{Berarducci2004AnEV,
  title={An effective version of Wilkie's theorem of the complement and some effective o-minimality results},
  author={A. Berarducci and Tamara Servi},
  journal={Ann. Pure Appl. Log.},
  year={2004},
  volume={125},
  pages={43-74}
}
Abstract Wilkie (Selecta Math. (N.S.) 5 (1999) 397) proved a “theorem of the complement” which implies that in order to establish the o-minimality of an expansion of R with C∞ functions it suffices to obtain uniform (in the parameters) bounds on the number of connected components of quantifier free definable sets. He deduced that any expansion of R with a family of Pfaffian functions is o-minimal. We prove an effective version of Wilkie's theorem of the complement, so in particular given an… Expand
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