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Book Review

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Book Information

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

References:

[Co]
M. Coste: Topological Types of Fewnomials. Singularities Symposium - {\L}ojasiewicz 70. Banach Center Pub. 44, Polish Acad. Sci. (1998), 81-92. CMP 99:09

[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

[KnPiSt]
J.F. Knight, A. Pillay, C. Steinhorn: Definable Sets in Ordered Structures. II. Trans. Amer. Math. Soc. 295 (1986), 563-605. MR 88b:03050b

[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.

Additional Information:

Reviewer(s):
Michel Coste
Affiliation: University of Rennes
Email: coste@univ-rennes1.fr

Review Information:
Journal: Bull. Amer. Math. Soc. 36 (1999), 523-527.

MSC (1991): Primary 32B20, 14P10, 57Q25, 57R05, 58A35
DOI: 10.1090/S0273-0979-99-00793-4
PII: S 0273-0979(99)00793-4
Posted: July 27, 1999
Copyright of article: Copyright 1999, American Mathematical Society

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