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A generalization of Wilkie's theorem of the complement, and an application to Pfaffian closure

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Abstract.

Using a modification of Wilkie's recent proof of o-minimality for Pfaffian functions, we give an invariant characterization of o-minimal expansions of $\Bbb R$. We apply this to construct the Pfaffian closure of an arbitrary o-minimal expansion of $\Bbb R$.

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Authors and Affiliations

  1. Dept. of Computer Science, University of Bonn, D-53117 Bonn, Germany, e-mail: marek@cs.uni-bonn.de, , , , , , DE

    M. Karpinski

  2. Mathematical Institute, University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom, e-mail: angus@maths.ed.ac.uk, , , , , , EN

    A. Macintyre

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  1. M. Karpinski
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  2. A. Macintyre
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Karpinski, M., Macintyre, A. A generalization of Wilkie's theorem of the complement, and an application to Pfaffian closure. Sel. math., New ser. 5, 507–516 (1999). https://doi.org/10.1007/s000290050055

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  • DOI: https://doi.org/10.1007/s000290050055

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