Analytic cell decomposition of sets definable in the structure ℝexp
Ta Lê Loi
Annales Polonici Mathematici, Tome 60 (1994), p. 255-266 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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

Publié le : 1994-01-01
EUDML-ID : urn:eudml:doc:262499 
@article{bwmeta1.element.bwnjournal-article-apmv59z3p255bwm,
     author = {Ta L\^e Loi},
     title = {Analytic cell decomposition of sets definable in the structure $$\mathbb{R}$\_{exp}$
            },
     journal = {Annales Polonici Mathematici},
     volume = {60},
     year = {1994},
     pages = {255-266},
     zbl = {0806.32001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv59z3p255bwm}
}

Ta Lê Loi. Analytic cell decomposition of sets definable in the structure $ℝ_{exp}$
            . Annales Polonici Mathematici, Tome 60 (1994) pp. 255-266. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv59z3p255bwm/

[000] [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. | Zbl 0435.32006

[001] [2] L. van den Dries, Tame topology and O-minimal structures, mimeographed notes, 1991.

[002] [3] L. van den Dries and C. Miller, On the real exponential field with restricted analytic functions, Israel J. Math. 85 (1994), 19-56. | Zbl 0823.03017

[003] [4] A. G. Khovanskiĭ, On a class of systems of transcendental equations, Dokl. Akad. Nauk SSSR 255 (1980), 804-807 (in Russian).

[004] [5] A. G. Khovanskiĭ, Fewnomials, Transl. Math. Monographs 88, Amer. Math. Soc., 1991.

[005] [6] J. Knight, A. Pillay and C. Steinhorn, Definable sets in ordered structures. II, Trans. Amer. Math. Soc. 295 (1986), 593-605. | Zbl 0662.03024

[006] [7] T. L. Loi, Ck-regular points of sets definable in the structure ℝexp, preprint, 1992.

[007] [8] S. Łojasiewicz, Ensembles Semi-Analytiques, mimeographed notes, I.H.E.S., Bures-sur-Yvette, 1965.

[008] [9] J. C. Tougeron, Sur certaines algèbres de fonctions analytiques, Séminaire de géométrie algébrique réelle, Paris VII, 1986.

[009] [10] J. C. Tougeron, Algèbres analytiques topologiquement noethériennes. Théorie de Khovanskiĭ, Ann. Inst. Fourier (Grenoble) 41 (4) (1991), 823-840.

[010] [11] A. J. Wilkie, Some model completeness results for expansions of the ordered field of real numbers by Pfaffian functions, preprint, 1991.

[011] [12] A. J. Wilkie, Model completeness results for expansions of the real field II: The exponential function, manuscript, 1991.