On some global semianalytic sets

Abdelhafed Elkhadiri[1]

  • [1] Department of Mathematics Faculty of Sciences University Ibn Tofail B.P. 133, Kénitra, Morocco

Annales de l’institut Fourier (2013)

  • Volume: 63, Issue: 5, page 1771-1791
  • ISSN: 0373-0956

Abstract

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We give some structures without quantifier elimination but in which the closure, and hence the interior and the boundary, of a quantifier free definable set is also a quantifier free definable set.

How to cite

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Elkhadiri, Abdelhafed. "On some global semianalytic sets." Annales de l’institut Fourier 63.5 (2013): 1771-1791. <http://eudml.org/doc/275485>.

@article{Elkhadiri2013,
abstract = {We give some structures without quantifier elimination but in which the closure, and hence the interior and the boundary, of a quantifier free definable set is also a quantifier free definable set.},
affiliation = {Department of Mathematics Faculty of Sciences University Ibn Tofail B.P. 133, Kénitra, Morocco},
author = {Elkhadiri, Abdelhafed},
journal = {Annales de l’institut Fourier},
keywords = {Quantifiers elimination - semi-analytic sets - semi-algebraic sets; quantifiers elimination; semi-analytic sets; semi-algebraic sets},
language = {eng},
number = {5},
pages = {1771-1791},
publisher = {Association des Annales de l’institut Fourier},
title = {On some global semianalytic sets},
url = {http://eudml.org/doc/275485},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Elkhadiri, Abdelhafed
TI - On some global semianalytic sets
JO - Annales de l’institut Fourier
PY - 2013
PB - Association des Annales de l’institut Fourier
VL - 63
IS - 5
SP - 1771
EP - 1791
AB - We give some structures without quantifier elimination but in which the closure, and hence the interior and the boundary, of a quantifier free definable set is also a quantifier free definable set.
LA - eng
KW - Quantifiers elimination - semi-analytic sets - semi-algebraic sets; quantifiers elimination; semi-analytic sets; semi-algebraic sets
UR - http://eudml.org/doc/275485
ER -

References

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  1. Lou van den Dries, Chris Miller, On the real exponential field with restricted analytic functions, Israel J. Math. 85 (1994), 19-56 Zbl0823.03017MR1264338
  2. A. Elkhadiri, J.-Cl. Tougeron, Familles noethériennes de modules sur k [ [ x ] ] et applications, Bull. Sci. math. 120 (1996), 253-292 Zbl0858.13009MR1399844
  3. A. Gabrielov, Complements of subanalytic sets and existential formulas for analytic functions, Invent. Math. 125 (1996), 1-12 Zbl0851.32009MR1389958
  4. S. Łojasiewicz, Ensembles semi-analytiques, (1965), IHES, Bures-sur-Yvette, France Zbl0241.32005
  5. J.- Cl. Tougeron, Idéaux de fonctions différentiables, (1971), Springer Verlag, Ergebnisse der Mathematik Zbl0251.58001MR415667
  6. Lou van den Dries, Tame topology and o-minimal structures, 248, Cambridge University Press Zbl0953.03045MR1633348
  7. Lou van den Dries, Remarks on Tarski’s problem concerning ( ℝ , + , . , exp ) , G. Lolli et al. (eds.), logic Colloquium ’82 (1984), 97-121, North-Holland, Amesterdam Zbl0585.03006
  8. Lou van den Dries, Chris Miller, Geometric categories and o-minimal structures, Duke Math. J. 84 (1996) Zbl0889.03025MR1404337
  9. A. J. Wilkie, Model completenes results for expansions of the ordered field of real numbers by restricted pfaffian functions and the exponential function, Journal of the American Mathematical Society 9 (October 1996) Zbl0892.03013MR1398816

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