Abstract
Let \({\mathcal {M}}\) be a dense o-minimal structure, \({\mathcal {N}}\) an unstable structure interpretable in \({\mathcal {M}}\). Then there exists X, definable in \({\mathcal {N}^{eq}}\), such that X, with the induced \({\mathcal {N}}\)-structure, is linearly ordered and o-minimal with respect to that ordering. As a consequence we obtain a classification, along the lines of Zilber’s trichotomy, of unstable þ-minimal types in structures interpretable in o-minimal theories.
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A. Hasson’s work was supported by the EPSRC grant no. EP C52800X 1.
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Hasson, A., Onshuus, A. Unstable structures definable in o-minimal theories. Sel. Math. New Ser. 16, 121–143 (2010). https://doi.org/10.1007/s00029-010-0018-y
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DOI: https://doi.org/10.1007/s00029-010-0018-y