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Construction d'un groupe dans les structures C-minimales

Published online by Cambridge University Press:  12 March 2014

Fares Maalouf*
Affiliation:
Equipe de Logique Mathématique, CNRS-UFR de Mathématiques, Université Paris7, 175 Rue du Chevaleret 75013 Paris, France, E-mail: [email protected]

Abstract

We will study some aspects of the local structure of models of certain C-minimal theories. We will prove (theorem 19) that, in a sufficiently saturated C-minimal structure in which the algebraic closure has the exchange property and which is locally modular, we can construct an infinite type-definable group around any non trivial point (a term to be defined later).

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2008

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References

RÉFÉRENCES

[1]Adeleke, S. A. and Neumann, P. M., Relations related to betweenness: theire structures and automorphisms, vol. 131, Memoirs of the American Mathematical Society, no. 623, 1998.Google Scholar
[2]Hrushovski, E., A new strongly o-minimal set, Annals of Pure and Applied Logic, vol. 62 (1993), pp. 147166.CrossRefGoogle Scholar
[3]Loveys, J. and Peterzil, Y., Linear o-minimal structures, Israel Journal of Mathematics, vol. 81 (1993), pp. 130.CrossRefGoogle Scholar
[4]Macpherson, D. and Haskell, D., Cell decompositions of C-minimal structures, Annals of Pure and Applied Logic, vol. 66 (1994), pp. 113162.Google Scholar
[5]Macpherson, D. and Steinhorn, C., On variants of o-minimality, Annals of Pure and Applied Logic, vol. 79 (1996), pp. 165209.CrossRefGoogle Scholar
[6]Mekler, A., Rubin, M., and Steinhorn, C., Dedekind completeness and the algebraic complexity of o-minimal structures, Canadian Journal of Mathematics, vol. 44 (1992), pp. 843855.CrossRefGoogle Scholar
[7]Peterzil, Y., Constructing a group interval in o-minimal structures, Journal of Pure and Applied Algebra, vol. 94 (1994), pp. 85100.CrossRefGoogle Scholar
[8]Peterzil, Y. and Starchenko, S., A trichotomy theorem for o-minimal structures, Proceedings of the London Mathematical Society, vol. 77 (1998), pp. 481523.CrossRefGoogle Scholar
[9]Zilber, B. and Hrushovski, E., Zariski geometries, Journal of the American Mathematical Society, vol. 9 (1996), pp. 156.Google Scholar