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An o-minimal structure without mild parameterization

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2011

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http://nbn-resolving.de/urn:nbn:de:bsz:352-171635
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https://doi.org/10.1016/j.apal.2010.11.004
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Annals of Pure and Applied Logic. 2011, 162(6), pp. 409-418. ISSN 0168-0072. Available under: doi: 10.1016/j.apal.2010.11.004

Zusammenfassung

We prove, by explicit construction, that not all sets definable in polynomially bounded o-minimal structures have mild parameterization. Our methods do not depend on the bounds particular to the definition of mildness and therefore our construction is also valid for a generalized form of parameterization, which we call G-mild. Moreover, we present a cell decomposition result for certain o-minimal structures which may be of independent interest. This allows us to show how our construction can produce polynomially bounded, model complete expansions of the real ordered field which, in addition to lacking G-mild parameterization, nonetheless still have analytic cell decomposition.

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510 Mathematik

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Polynomially bounded structures, Rational-points, Entropy, Number

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ISO 690THOMAS, Margaret E. M., 2011. An o-minimal structure without mild parameterization. In: Annals of Pure and Applied Logic. 2011, 162(6), pp. 409-418. ISSN 0168-0072. Available under: doi: 10.1016/j.apal.2010.11.004
BibTex
@article{Thomas2011omini-17163,
  year={2011},
  doi={10.1016/j.apal.2010.11.004},
  title={An o-minimal structure without mild parameterization},
  number={6},
  volume={162},
  issn={0168-0072},
  journal={Annals of Pure and Applied Logic},
  pages={409--418},
  author={Thomas, Margaret E. M.}
}
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