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Book Review

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Book Information

Author(s): Lou van den Dries
Title: Tame topology and o-minimal structures
Additional book information: Cambridge Univ. Press, New York, 1998, x + 180, $39.95, 0-521-59838-9

References:

[1]
R. Benedetti and J.-J. Risler, Real algebraic and semi-algebraic sets, Hermann, 1990. MR 91j:14045

[2]
E. Bierstone and P. Milman, Semianalytic and subanalytic sets, IHES Publ. Math 67 (1988), 5-42. MR 89k:32011

[3]
J. Bochnak, M. Coste and M.-F. Roy, Real Algebraic Geometry, Springer Verlag, 1998. MR 2000a:14067

[4]
L. van den Dries, Remarks on Tarski's problem concerning $(\mathbf{R},+,\cdot,\exp)$, in Logic Colloquium '82, G. Lolli, G. Longo and A. Marcja, eds., North-Holland, 1984, 97-121. MR 86g:03052

[5]
L. van den Dries, A generalization of the Tarski-Seidenberg theorem, and some nondefinability results, Bull. AMS 15 (1986), 189-193. MR 88b:03048

[6]
L. van den Dries, A. Macintyre and D. Marker, The elementary theory of restricted analytic fields with exponentiation, Ann. Math 140 (1994), 183-205. MR 95k:12015

[7]
L. van den Dries and C. Miller, Geometric categories and o-minimal structures, Duke Math. J. 84 (1996), 497-540. MR 97i:32008

[8]
L. van den Dries and P. Speissegger, The real field with convergent generalized power series, Trans. AMS 350 (1998), 4377-4421. MR 99a:03036

[9]
L. van den Dries and P. Speissegger, The field of reals with multisummable series and the exponential function, Proc. London Math. Soc., to appear.

[10]
A. Grothendieck, Esquisse d'un Programme, in [17], 5-48. MR 99c:14034

[11]
A. Khovanskii, On a class of systems of transcendental equations, Sov. Math. Dokl. 2 (1980) 762-765. MR 82a:14006

[12]
J. Knight, A. Pillay and C. Steinhorn, Definable sets in ordered structures II, Trans. AMS 295 (1986) 593-605. MR 88b:03050b

[13]
Y. Peterzil and S. Starchenko, A trichotomy theorem for o-minimal structures, Proc. London Math. Soc. 77 (1998), 481-523. MR 2000b:03123

[14]
Y. Peterzil, A. Pillay and S. Starchenko, Simple algebraic and semialgebraic groups over real closed fields, Trans. AMS, to appear.

[15]
A. Pillay, On groups and fields definable in o-minimal structures, J. Pure. Appl. Algebra 53 (1988), 239-255. MR 89i:03069

[16]
A. Pillay and C. Steinhorn, Definable sets in ordered structures I, Trans. AMS 295 (1986), 565-592. MR 88b:03050a

[17]
L. Schneps and P. Lochak, Geometric Galois Actions: I. Around Grothendieck's Esquisse d'un Programme, Cambridge Univ. Press, 1997. MR 98e:14003

[18]
P. Speissegger, The Pfaffian closure of an o-minimal structure, J. Reine Angew. Math. 508 (1999), 198-211. CMP 99:09

[19]
B. Tessier, Tame and stratified objects, in [17], 231-243.

[20]
A. Wilkie, Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function, J. AMS 9 (1996), 1051-1094. MR 98j:03052
[21]
A. Wilkie, A general theorem of the complement and some new o-minimal structures, preprint, 1996.

Additional Information:

Reviewer(s):
David Marker
Affiliation: University of Illinois at Chicago
Email: marker@math.uic.edu

Review Information:
Journal: Bull. Amer. Math. Soc. 37 (2000), 351-357.

MSC (2000): Primary 03C64; Secondary 14P10, 14P15
DOI: 10.1090/S0273-0979-00-00866-1
PII: S 0273-0979(00)00866-1
Posted: March 2, 2000
Copyright of article: Copyright 2000, American Mathematical Society

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