Verdier and strict Thom stratifications in o-minimal structures

Illinois Journal of Mathematics

Volumn 42, Issue 2, 1998, Pages 347-356

  Loi, Ta Lê ^a  

^a UNIVERSITY OF DALAT   (Viet Nam)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032104998     PISSN: 00192082     EISSN: None     Source Type: Journal    
DOI: 10.1215/ijm/1256045049     Document Type: Article

References (21)

1. K. Bekka, Regular stratification of subanalytic sets, Bull. London Math. Soc. 25 (1993), 7-16.
2. H. Brodersen and D. Trotman, Whitney (b)-regularity is weaker than Kuo's ratio test for real algebraic stratifications, Math. Scand. 45 (1979), 27-34.
3. L. van den Dries, Tame topology and o-minimal structures, LMS Lecture Notes, Cambridge University Press, to appear.
4. L. van den Dries and C. Miller, On the real exponential field with restricted analytic functions, Israel J. Math. 85 (1994), 19-56.
5. _, Geometric Categories and o-minimal structures, Duke Math. J. 84 (1996), 497-540.
6. L. van den Dries and P. Speissegger, The field of reals with multisummable series and the exponential function, preprint, 1997.
7. Z. Denkowska and K. Wachta, Une construction de la stratifications sous-analytiques avec la condition (w), Bull. Polish Acad. Math. 35 (1987), 401-405.
8. T. C. Kuo, The ratio test for analytic Whitney stratifications, Proceedings of Liverpool Symposium I, Lecture Notes 192, Springer verlag, 1971.
9. K. Kurdyka and A. Parusiński, (wf)-stratification of subanalytic functions and the Lojasiewicz inequality, C.R. Acad. Sci. Paris Série I 318 (1994), 129-133.
10. K. Kurdyka and G. Raby, Densité des ensembles sous-analytiques, Ann. Inst. Fourier 39 (1989), 735-771.
11. exp, Banach Center Publications, Vol 33, 1996, 401-409.
12. _, Thom sratification for functions definable in o-minimal structures on (R, +, ̇), C.R. Acad. Sci. Paris Série I 324 (1997) 1391-1394.
13. J. M. Lion and J. P. Rolin, Théorème de Gabrielov et fonctions log-exp-algebriques, preprint, 1996.
14. S. Lojasiewicz, J. Stasica and K. Wachta, Stratifications sous-analytiques. Condition de Verdier, Bull. Polish Acad. Math. 34 (1986), 531-539.
15. C. Miller, Exponentiation is hard to avoid, Proc. Amer. Math. Soc. 122 (1994), 257-259.
16. _, Expansions of the real field with power functions, Ann. Pure Appl. Logic 68 (1994), 79-84.
17. M. Shiota, "Geometry of subanalytic and semianalytic sets, Abstract" in Real analytic and algebraic geometry (F. Broglia et al. eds.), W. de Gruyter, 1995, 251-275.
18. J. L. Verdier, Stratification de Whitney et theoreme de Bertini-Sard, Invent. Math. 36 (1976), 295-312.
19. A. Wilkie, Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function, J. Amer. Math. Soc. 9 (1996), 1051-1094.
20. _, A general theorem of the complement and some new o-minimal structures, manuscript, 1996.
21. H. Whitney, Tangents to an analytic variety, Ann. of Math. 81 ( 1965), 496-549.