The aim of this paper is to prove that every subset of definable from addition, multiplication and exponentiation admits a stratification satisfying Whitney’s conditions a) and b).
@article{bwmeta1.element.bwnjournal-article-bcpv33z1p401bwm, author = {Loi, Ta}, title = {Whitney stratification of sets definable in the structure $$\mathbb{R}$\_{exp}$ }, journal = {Banach Center Publications}, volume = {37}, year = {1996}, pages = {401-409}, zbl = {0904.14030}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv33z1p401bwm} }
Loi, Ta. Whitney stratification of sets definable in the structure $ℝ_{exp}$ . Banach Center Publications, Tome 37 (1996) pp. 401-409. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv33z1p401bwm/
[000] [1] L. van den Dries, Tame topology and O-minimal structures, mimeographed notes (1991).
[001] [2] L. van den Dries and C. Miller, The field of reals with restricted analytic functions and unrestricted exponentiation, Israel J. Math. (1991).
[002] [3] R. M. Goresky, Triangulation of stratified objects, Proc. Amer. Math. Soc. 72 (1978), 193-200. | Zbl 0392.57001
[003] [4] A. G. Khovanskiĭ, Fewnomials, Transl. Math. Monographs 88, Amer. Math. Soc., 1991.
[004] [5] T. L. Loi, thesis, Jagiellonian University, Kraków 1993.
[005] [6] T. L. Loi, Analytic cell decomposition of sets definable in the structure , Ann. Polon. Math. 59 (1994), 255-266. | Zbl 0806.32001
[006] [7] T. L. Loi, On the global Łojasiewicz inequalities for the class of analytic logarithmico-exponential functions, C. R. Acad. Sci. Paris Sér. I 318 (1994), 543-548. | Zbl 0804.32008
[007] [8] S. Łojasiewicz, Ensembles Semi-Analytiques, I.H.E.S., Bures-sur-Yvette, 1965.
[008] [9] A. J. Wilkie, Some model completeness results for expansions of the ordered field of real numbers by Pfaffian functions, preprint, 1991.
[009] [10] A. J. Wilkie, Model completeness results for expansions of the real field II: The exponential function, manuscript, 1991.