On some global semianalytic sets
Annales de l'Institut Fourier, Volume 63 (2013) no. 5, pp. 1771-1791.

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.

On donne quelques structures n’ayant pas l’élimination des quantificateurs, mais dans lesquelles l’adhérence, et donc l’intérieur et le bord, d’un ensemble défini sans quantificateur est encore un ensemble défini sans quantificateur.

DOI: 10.5802/aif.2814
Classification: 03C10, 32B20
Keywords: Quantifiers elimination - semi-analytic sets - semi-algebraic sets.
Mot clés : Ensembles semianalytiques - Ensembles semialgébriques - Elimination des quantificateurs.

Elkhadiri, Abdelhafed 1

1 Department of Mathematics Faculty of Sciences University Ibn Tofail B.P. 133, Kénitra, Morocco
@article{AIF_2013__63_5_1771_0,
     author = {Elkhadiri, Abdelhafed},
     title = {On some global semianalytic sets},
     journal = {Annales de l'Institut Fourier},
     pages = {1771--1791},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {63},
     number = {5},
     year = {2013},
     doi = {10.5802/aif.2814},
     mrnumber = {3186508},
     zbl = {06284532},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2814/}
}
TY  - JOUR
AU  - Elkhadiri, Abdelhafed
TI  - On some global semianalytic sets
JO  - Annales de l'Institut Fourier
PY  - 2013
SP  - 1771
EP  - 1791
VL  - 63
IS  - 5
PB  - Association des Annales de l’institut Fourier
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.2814/
DO  - 10.5802/aif.2814
LA  - en
ID  - AIF_2013__63_5_1771_0
ER  - 
%0 Journal Article
%A Elkhadiri, Abdelhafed
%T On some global semianalytic sets
%J Annales de l'Institut Fourier
%D 2013
%P 1771-1791
%V 63
%N 5
%I Association des Annales de l’institut Fourier
%U https://aif.centre-mersenne.org/articles/10.5802/aif.2814/
%R 10.5802/aif.2814
%G en
%F AIF_2013__63_5_1771_0
Elkhadiri, Abdelhafed. On some global semianalytic sets. Annales de l'Institut Fourier, Volume 63 (2013) no. 5, pp. 1771-1791. doi : 10.5802/aif.2814. https://aif.centre-mersenne.org/articles/10.5802/aif.2814/

[1] van den Dries, Lou; Miller, Chris On the real exponential field with restricted analytic functions, Israel J. Math., Volume 85 (1994), pp. 19-56 | DOI | MR | Zbl

[2] Elkhadiri, A.; Tougeron, J.-Cl. Familles noethériennes de modules sur k[[x]] et applications, Bull. Sci. math., Volume 120 (1996), pp. 253-292 | MR | Zbl

[3] Gabrielov, A. Complements of subanalytic sets and existential formulas for analytic functions, Invent. Math., Volume 125 (1996) no. 1, pp. 1-12 | DOI | MR | Zbl

[4] Łojasiewicz, S. Ensembles semi-analytiques, IHES, Bures-sur-Yvette, France, 1965

[5] Tougeron, J.- Cl. Idéaux de fonctions différentiables, Springer Verlag, Ergebnisse der Mathematik, 1971 | MR | Zbl

[6] van den Dries, Lou Tame topology and o-minimal structures, 248, Cambridge University Press | MR | Zbl

[7] van den Dries, Lou Remarks on Tarski’s problem concerning (,+,.,exp), G. Lolli et al. (eds.), logic Colloquium ’82, North-Holland, Amesterdam, 1984, pp. 97-121 | Zbl

[8] van den Dries, Lou; Miller, Chris Geometric categories and o-minimal structures, Duke Math. J., Volume 84 (1996) no. 2 | DOI | MR | Zbl

[9] Wilkie, A. J. 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, Volume 9 (October 1996) no. 4 | MR | Zbl

Cited by Sources: