Theorems of the Complement

@inproceedings{Fornasiero2012TheoremsOT,
  title={Theorems of the Complement},
  author={A. Fornasiero and Tamara Servi},
  year={2012}
}
This is an expository paper on a Theorem of the Complement, due to Wilkie, and its generalisations. Wilkie (Sel Math (NS) 5:397–421, 1999) gave necessary and sufficient conditions for an expansion of the real field by C-infinity functions to be o-minimal. Karpinski and Macintyre (Sel Math (NS) 5:507–516, 1999) weakened the original smoothness hypotheses of Wilkie’s theorem. Here we exhibit the proof of a generalised Wilkie’s result, where we further weaken the smoothness assumptions and show… Expand
4 Citations
Definably complete Baire structures
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Remarks on expansions of the real field: tameness, Hardy fields and smooth rings.
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An analogue of the Baire category theorem
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