Remote Access Journal of the American Mathematical Society
Green Open Access

Journal of the American Mathematical Society

ISSN 1088-6834(online) ISSN 0894-0347(print)

 
 

 

Model completeness results for expansions
of the ordered field of real numbers
by restricted Pfaffian functions
and the exponential function


Author: A. J. Wilkie
Journal: J. Amer. Math. Soc. 9 (1996), 1051-1094
MSC (1991): Primary 03C10
DOI: https://doi.org/10.1090/S0894-0347-96-00216-0
MathSciNet review: 1398816
Full-text PDF

References | Similar Articles | Additional Information

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

  • 1. J. Bridge, Begining model theory, Oxford Univ. Press, 1977. MR 58:27171
  • 2. B. I. Dahn, The limit behaviour of exponential terms, Fund. Math. 124 (1984), 169--186. MR 86f:03058
  • 3. J. Denef and L. van den Dries, $P$-adic and real subanalytic sets, Ann. of Math. 128 (1988), 79--138. MR 89k:03034
  • 4. J. Dieudonné, Foundations of modern analysis, Academic Press, San Diego, 1969. MR 50:1782
  • 5. A. Gabrielov, Projections of semi-analytic sets, Functional Anal. Appl. 2 (1968), 282--291. MR 39:7137
  • 6. A. G. Khovanskii, On a class of systems of transcendental equations, Soviet Math. Dokl. 22 (1980), 762--765. MR 82a:14006
  • 7. J. F. Knight, A. Pillay, and C. Steinhorn, Definable sets in ordered structures, II, Trans. Amer. Math. Soc. 295 (1986), 593--605. MR 88b:03050b
  • 8. S. {\L}ojasiewicz, Ensembles semi-analytiques, mimeographed notes, IHES, 1965.
  • 9. L. Mirsky, Introduction to linear algebra, Oxford Univ. Press, 1955. MR 17:573a
  • 10. A. Pillay and C. Steinhorn, Definable sets in ordered structures. I Trans. Amer. Math. Soc. 295 (1986), 565--592. MR 88b:03050a
  • 11. A. Tarski, A decision method for elementary algebra and geometry, 2nd revised ed., Berkeley and Los Angeles, 1951. MR 13:423a
  • 12. L. van den Dries, Remarks on Tarski's problem concerning $\langle R,+,\cdot ,\exp \rangle$, Logic Colloquium 1982, North Holland, 1984, p. 97--121. MR 86b:03052
  • 13. ------, A generalization of the Tarski-Seidenberg theorem, and some nondefinability results, Bull. Amer. Math. Soc. (N.S.) 15 (1986), 189--193. MR 88b:03048
  • 14. ------, On the elementary theory of restricted elementary functions, J. Symbolic Logic 53 (1988), 796--808. MR 89i:03074
  • 15. ------, Tame topology and $0$-minimal structures, mimeographed notes, University of Illinois at Urbana-Champaign, 1991.
  • 16. A. J. Wilkie, On the theory of the real exponential field, Illinois J. Math. 33 (1989), 384--408. MR 90i:03042
  • 17. H. Wolter, On the model theory of exponential fields (survey), Logic Colloquium 1984, North-Holland, 1986, pp. 343--353. MR 88a:03082

Similar Articles

Retrieve articles in Journal of the American Mathematical Society with MSC (1991): 03C10

Retrieve articles in all journals with MSC (1991): 03C10


Additional Information

A. J. Wilkie
Affiliation: Mathematical Institute, 24-29 St. Giles, Oxford OX1 3LB, United Kingdom
Email: wilkie@maths.oxford.ac.uk

DOI: https://doi.org/10.1090/S0894-0347-96-00216-0
Received by editor(s): July 28, 1992
Received by editor(s) in revised form: June 29, 1995
Article copyright: © Copyright 1996 American Mathematical Society

American Mathematical Society