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Transfer methods for o-minimal topology

  • Alessandro Berarducci (a1) and Margarita Otero (a2)
Abstract
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 φR 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.

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[2]A. Berarducci and M. Otero , Intersection theory for o-minimal manifolds, Annals of Pure and Applied Logic, vol. 107 (2001), pp. 87119.

[8]D. E. Galewski and R. J. Stern , Classification of simplicial triangulations of topological manifolds, Annals of Mathematics, vol. 111 (1980), pp. 134.

[12]J. W. Milnor and J. D. Stasheff , Characteristic classes, Annals of Mathematics Studies, Princeton University Press, Princeton, 1974.

[13]Y. Peterzil and C. Steinhorn , Definable compactness and definable subgroups of o-minimal groups, Journal of the London Mathematical Society, vol. 59 (1999), pp. 769786.

[14]A. Pillay , On groups and fields definable in o-minimal structures. Journal of Pure and Applied Algebra, vol. 53 (1988), pp. 239255.

[15]M. Shiota , Geometry of subanalytic and semialgebraic sets, Progress in Mathematics, Birkhäuser, Boston, 1997.

[16]A. Strzebonski , Euler characteristic in semialgebraic and other o-minimal structures. Journal of Pure and Applied Algebra, vol. 96 (1994), pp. 173201.

[18]L. van den Dries , Tame topology and o-minimal structures, London Mathematical Society Lecture Notes Series, vol. 248, Cambridge University Press, 1998.

[19]J. W. Vick , Homology theory, Springer-Verlag, 1994.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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