Analytic cell decomposition of sets definable in the structure ℝ e x p

Ta Lê Loi

Annales Polonici Mathematici (1994)

  • Volume: 59, Issue: 3, page 255-266
  • ISSN: 0066-2216

Abstract

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We prove that every set definable in the structure ℝ e x p can be decomposed into finitely many connected analytic manifolds each of which is also definable in this structure.

How to cite

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Ta Lê Loi. "Analytic cell decomposition of sets definable in the structure $ℝ_{exp}$." Annales Polonici Mathematici 59.3 (1994): 255-266. <http://eudml.org/doc/262499>.

@article{TaLêLoi1994,
abstract = {We prove that every set definable in the structure $ℝ_\{exp\}$ can be decomposed into finitely many connected analytic manifolds each of which is also definable in this structure.},
author = {Ta Lê Loi},
journal = {Annales Polonici Mathematici},
keywords = {𝒟-sets; Wilkie's Theorem; semianalytic sets; analytic cell decomposition; Tarski's system; Tarski system},
language = {eng},
number = {3},
pages = {255-266},
title = {Analytic cell decomposition of sets definable in the structure $ℝ_\{exp\}$},
url = {http://eudml.org/doc/262499},
volume = {59},
year = {1994},
}

TY - JOUR
AU - Ta Lê Loi
TI - Analytic cell decomposition of sets definable in the structure $ℝ_{exp}$
JO - Annales Polonici Mathematici
PY - 1994
VL - 59
IS - 3
SP - 255
EP - 266
AB - We prove that every set definable in the structure $ℝ_{exp}$ can be decomposed into finitely many connected analytic manifolds each of which is also definable in this structure.
LA - eng
KW - 𝒟-sets; Wilkie's Theorem; semianalytic sets; analytic cell decomposition; Tarski's system; Tarski system
UR - http://eudml.org/doc/262499
ER -

References

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  1. [1] Z. Denkowska, S. Łojasiewicz and J. Stasica, Certaines propriétés élémentaires des ensembles sous-analytiques, Bull. Acad. Polon. Sci. Sér. Sci. Math. 27 (1979), 529-536. Zbl0435.32006
  2. [2] L. van den Dries, Tame topology and O-minimal structures, mimeographed notes, 1991. 
  3. [3] L. van den Dries and C. Miller, On the real exponential field with restricted analytic functions, Israel J. Math. 85 (1994), 19-56. Zbl0823.03017
  4. [4] A. G. Khovanskiĭ, On a class of systems of transcendental equations, Dokl. Akad. Nauk SSSR 255 (1980), 804-807 (in Russian). 
  5. [5] A. G. Khovanskiĭ, Fewnomials, Transl. Math. Monographs 88, Amer. Math. Soc., 1991. 
  6. [6] J. Knight, A. Pillay and C. Steinhorn, Definable sets in ordered structures. II, Trans. Amer. Math. Soc. 295 (1986), 593-605. Zbl0662.03024
  7. [7] T. L. Loi, C k -regular points of sets definable in the structure ℝ e x p , preprint, 1992. 
  8. [8] S. Łojasiewicz, Ensembles Semi-Analytiques, mimeographed notes, I.H.E.S., Bures-sur-Yvette, 1965. 
  9. [9] J. C. Tougeron, Sur certaines algèbres de fonctions analytiques, Séminaire de géométrie algébrique réelle, Paris VII, 1986. 
  10. [10] J. C. Tougeron, Algèbres analytiques topologiquement noethériennes. Théorie de Khovanskiĭ, Ann. Inst. Fourier (Grenoble) 41 (4) (1991), 823-840. 
  11. [11] A. J. Wilkie, Some model completeness results for expansions of the ordered field of real numbers by Pfaffian functions, preprint, 1991. 
  12. [12] A. J. Wilkie, Model completeness results for expansions of the real field II: The exponential function, manuscript, 1991. 

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