Whitney stratification of sets definable in the structure ℝ e x p

Ta Loi

Banach Center Publications (1996)

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

Abstract

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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).

How to cite

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Loi, 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

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  1. [1] L. van den Dries, Tame topology and O-minimal structures, mimeographed notes (1991). 
  2. [2] L. van den Dries and C. Miller, The field of reals with restricted analytic functions and unrestricted exponentiation, Israel J. Math. (1991). 
  3. [3] R. M. Goresky, Triangulation of stratified objects, Proc. Amer. Math. Soc. 72 (1978), 193-200. Zbl0392.57001
  4. [4] A. G. Khovanskiĭ, Fewnomials, Transl. Math. Monographs 88, Amer. Math. Soc., 1991. 
  5. [5] T. L. Loi, thesis, Jagiellonian University, Kraków 1993. 
  6. [6] T. L. Loi, Analytic cell decomposition of sets definable in the structure ℝ e x p , Ann. Polon. Math. 59 (1994), 255-266. Zbl0806.32001
  7. [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. [8] S. Łojasiewicz, Ensembles Semi-Analytiques, I.H.E.S., Bures-sur-Yvette, 1965. 
  9. [9] A. J. Wilkie, Some model completeness results for expansions of the ordered field of real numbers by Pfaffian functions, preprint, 1991. 
  10. [10] A. J. Wilkie, Model completeness results for expansions of the real field II: The exponential function, manuscript, 1991. 

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