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Preprint Number 89

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89. Alexander Berenstein
Lovely pairs and dense pairs of O-minimal structures
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Submission date: 13 October 2008. New expanded version of this paper is Preprint Nr 151, done in collaboration with E. Vassiliev.

Abstract:

We study the theory of Lovely pairs of thorn-rank one theories, in particular O-minimal theories. We show that the class of aleph_0-saturated dense pairs of O-minimal structures studied by van den Dries agrees with the corresponding class of lovely pairs. We also prove that the theory of lovely pairs of O-minimal structures is super-rosy of rank less than or equal to omega.

Mathematics Subject Classification: 03C64, 03C45

Keywords and phrases: O-minimality, rosy theories, lovely pairs.

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