# Analytic cell decomposition of sets definable in the structure ${\mathbb{R}}_{exp}$

Annales Polonici Mathematici (1994)

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

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topTa 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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- [2] L. van den Dries, Tame topology and O-minimal structures, mimeographed notes, 1991.
- [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] A. G. Khovanskiĭ, On a class of systems of transcendental equations, Dokl. Akad. Nauk SSSR 255 (1980), 804-807 (in Russian).
- [5] A. G. Khovanskiĭ, Fewnomials, Transl. Math. Monographs 88, Amer. Math. Soc., 1991.
- [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] T. L. Loi, ${C}^{k}$-regular points of sets definable in the structure ${\mathbb{R}}_{exp}$, preprint, 1992.
- [8] S. Łojasiewicz, Ensembles Semi-Analytiques, mimeographed notes, I.H.E.S., Bures-sur-Yvette, 1965.
- [9] J. C. Tougeron, Sur certaines algèbres de fonctions analytiques, Séminaire de géométrie algébrique réelle, Paris VII, 1986.
- [10] J. C. Tougeron, Algèbres analytiques topologiquement noethériennes. Théorie de Khovanskiĭ, Ann. Inst. Fourier (Grenoble) 41 (4) (1991), 823-840.
- [11] A. J. Wilkie, Some model completeness results for expansions of the ordered field of real numbers by Pfaffian functions, preprint, 1991.
- [12] A. J. Wilkie, Model completeness results for expansions of the real field II: The exponential function, manuscript, 1991.

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