# Whitney stratification of sets definable in the structure ${\mathbb{R}}_{exp}$

Banach Center Publications (1996)

- Volume: 33, Issue: 1, page 401-409
- ISSN: 0137-6934

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topLoi, Ta. "Whitney stratification of sets definable in the structure $ℝ_{exp}$." Banach Center Publications 33.1 (1996): 401-409. <http://eudml.org/doc/262755>.

@article{Loi1996,

abstract = {The aim of this paper is to prove that every subset of $ℝ^n$ definable from addition, multiplication and exponentiation admits a stratification satisfying Whitney’s conditions a) and b).},

author = {Loi, Ta},

journal = {Banach Center Publications},

keywords = {Whitney stratification; tangent space; real analytic set},

language = {eng},

number = {1},

pages = {401-409},

title = {Whitney stratification of sets definable in the structure $ℝ_\{exp\}$},

url = {http://eudml.org/doc/262755},

volume = {33},

year = {1996},

}

TY - JOUR

AU - Loi, Ta

TI - Whitney stratification of sets definable in the structure $ℝ_{exp}$

JO - Banach Center Publications

PY - 1996

VL - 33

IS - 1

SP - 401

EP - 409

AB - The aim of this paper is to prove that every subset of $ℝ^n$ definable from addition, multiplication and exponentiation admits a stratification satisfying Whitney’s conditions a) and b).

LA - eng

KW - Whitney stratification; tangent space; real analytic set

UR - http://eudml.org/doc/262755

ER -

## References

top- [1] L. van den Dries, Tame topology and O-minimal structures, mimeographed notes (1991).
- [2] L. van den Dries and C. Miller, The field of reals with restricted analytic functions and unrestricted exponentiation, Israel J. Math. (1991).
- [3] R. M. Goresky, Triangulation of stratified objects, Proc. Amer. Math. Soc. 72 (1978), 193-200. Zbl0392.57001
- [4] A. G. Khovanskiĭ, Fewnomials, Transl. Math. Monographs 88, Amer. Math. Soc., 1991.
- [5] T. L. Loi, thesis, Jagiellonian University, Kraków 1993.
- [6] T. L. Loi, Analytic cell decomposition of sets definable in the structure ${\mathbb{R}}_{e}xp$, Ann. Polon. Math. 59 (1994), 255-266. Zbl0806.32001
- [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. Zbl0804.32008
- [8] S. Łojasiewicz, Ensembles Semi-Analytiques, I.H.E.S., Bures-sur-Yvette, 1965.
- [9] A. J. Wilkie, Some model completeness results for expansions of the ordered field of real numbers by Pfaffian functions, preprint, 1991.
- [10] A. J. Wilkie, Model completeness results for expansions of the real field II: The exponential function, manuscript, 1991.

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