Journal of Symbolic Logic

Transfer methods for o-minimal topology

Alessandro Berarducci and Margarita Otero

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Abstract

Let M be an o-minimal expansion of an ordered field. Let φ be a formula in the language of ordered domains. In this note we establish some topological properties which are transferred from φM to φ and vice versa. Then, we apply these transfer results to give a new proof of a result of M. Edmundo—based on the work of A. Strzebonski—showing the existence of torsion points in any definably compact group defined in an o-minimal expansion of an ordered field.

Article information

Source
J. Symbolic Logic, Volume 68, Issue 3 (2003), 785- 794.

Dates
First available in Project Euclid: 17 July 2003

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1058448438

Digital Object Identifier
doi:10.2178/jsl/1058448438

Mathematical Reviews number (MathSciNet)
MR2004h:03082

Zentralblatt MATH identifier
1060.03059

Citation

Berarducci, Alessandro; Otero, Margarita. Transfer methods for o-minimal topology. J. Symbolic Logic 68 (2003), no. 3, 785-- 794. doi:10.2178/jsl/1058448438. https://projecteuclid.org/euclid.jsl/1058448438


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References

  • A. Berarducci and M. Otero Some examples of transfer methods for o-minimal structures, The Proceedings of the Meeting ``Spring Stage on Logic, Algebra and Geometry'', Caserta, Italy, 21--24 March 2000, preprint.
  • R. Brown Elements of modern topology, McGraw-Hill, London,1968.
  • G. W. Brumfield A Hopf fixed point theorem for semialgebraic maps, Real algebraic geometry, Proceedings of Rennes 1991, Lecture Notes in Mathematics, vol. 1524, Springer-Verlag,1992.
  • H. Delfs and M. Knebusch On the homology of algebraic varieties over real closed fields, Journal für die Reine und Angewandte Mathematik, vol. 335 (1982), pp. 122--163.
  • M. J. Edmundo O-minimal cohomology and definably compact definable groups, preprint, 2000 (revised version 2001).
  • D. E. Galewski and R. J. Stern Classification of simplicial triangulations of topological manifolds, Annals of Mathematics, vol. 111 (1980), pp. 1--34.
  • J. G. Hocking and G. S. Young Topology, Dover Publications, New York,1988.
  • J. Johns An open mapping for o-minimal structures, Journal of Symbolic Logic, vol. 66 (2001), pp. 1817--1820.
  • Y. Peterzil M. Otero and A. Pillay Groups and rings definable in o-minimal expansions of real closed fields, Bulletin of the London Mathematical Society, vol. 28 (1996), pp. 7--14.
  • J. W. Milnor and J. D. Stasheff Characteristic classes, Annals of Mathematics Studies, Princeton University Press, Princeton,1974.
  • Y. Peterzil and C. Steinhorn Definable compactness and definable subgroups of o-minimal groups, Journal of the London Mathematical Society, vol. 59 (1999), pp. 769--786.
  • A. Pillay On groups and fields definable in o-minimal structures, Journal of Pure and Applied Algebra, vol. 53 (1988), pp. 239--255.
  • M. Shiota Geometry of subanalytic and semialgebraic sets, Progress in Mathematics, Birkhäuser, Boston,1997.
  • A. Strzebonski Euler characteristic in semialgebraic and other o-minimal structures, Journal of Pure and Applied Algebra, vol. 96 (1994), pp. 173--201.
  • W. P. Thurston Three-dimensional geometry and topology, Princeton University Press,1997.
  • L. van den Dries Tame topology and o-minimal structures, London Mathematical Society Lecture Notes Series, vol. 248, Cambridge University Press,1998.
  • J. W. Vick Homology theory, Springer-Verlag,1994.
  • A. Woerheide O-minimal homology, Ph.D. thesis, University of Illinois at Urbana-Champaign,1996.