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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

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Book Information:

Author: M. Shiota
Title: Geometry of subanalytic and semialgebraic sets
Additional book information: Birkhäuser, Boston, MA, 1997, xii+431 pp., ISBN 0-8176-4000-2, $89.50

References [Enhancements On Off] (What's this?)

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  • [vdD] L. van den Dries: Tame Topology and O-minimal Structures. London Math. Soc. Lect. Notes 248. Cambridge Univ. Press 1998. CMP 98:15
  • [vdDMi] L. van den Dries, C. Miller: Geometric Categories and O-minimal Structures. Duke Math. J. 84 (1996), 497-540. MR 97i:32008
  • [Gial] C.G. Gibson et al.: Topological Stability of Smooth Mappings. Lecture Notes in Math. 552. Springer-Verlag 1976. MR 55:9151
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  • [Mu] J.R. Munkres: Elementary Differential Topology. Ann. of Math. Studies. Princeton Univ. Press 1963. MR 29:623
  • [PeSt] Y. Peterzil, S. Starchenko: A Trichotomy Theorem for O-minimal Structures. Proc. London Math. Soc. 77 (1998), 481-523. CMP 99:01
  • [PiSt] A. Pillay, C. Steinhorn: Definable Sets in Ordered Structures. I. Trans. Amer. Math. Soc. 295 (1986), 565-592. MR 88b:03050a
  • [Sh1] M. Shiota: Nash Manifolds. Lect. Notes Math. 1269. Springer-Verlag 1987. MR 89b:58011
  • [Sh2] M. Shiota: Thom's Conjecture on Triangulation of Maps. Sûrikaisekikenkyûsho Kôkyûroku No. 1050 (1998), 12-28. CMP 99:09
  • [Wi1] A. Wilkie: Model Completeness Results for Expansions of the Real Field by Restricted Pfaffian Functions and the Exponential Function. J. Amer. Math. Soc. 9 (1996), 1051-1094. MR 98j:03052
  • [Wi2] A. Wilkie: A General Theorem of the Complement and Some New O-minimal Structures. Preprint, 1996.

Review Information:

Reviewer: Michel Coste
Affiliation: University of Rennes
Journal: Bull. Amer. Math. Soc. 36 (1999), 523-527
MSC (1991): Primary 32B20, 14P10, 57Q25, 57R05, 58A35
Published electronically: July 27, 1999
Review copyright: © Copyright 1999 American Mathematical Society
American Mathematical Society