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Preprint Number 73

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73. Assaf Hasson and Alf Onshuus
Unstable structures definable in o-minimal theories

Submission date: 1 May 2007

Abstract: Let M be an o-minimal structure with elimination of imaginaries, N an unstable structure definable in M. Then there exists X, interpretable in N, such that X with all the structure induced from N is o-minimal. In particular X is linearly ordered. As part of the proof we show: Theorem 1: If the M-dimenson of N is 1 then any 1-N-type is either strongly stable or finite by o-minimal. Theorem 2: If N is N-minimal then it is 1-M-dimensional.

Mathematics Subject Classification: 03C64, 03C45

Keywords and phrases: o-minimality, dependent theories, NIP, thorn-forking.

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