Unstable structures definable in o-minimal theories

Let be a dense o-minimal structure, an unstable structure interpretable in . Then there exists X , definable in , such that X , with the induced -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 trich...

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Bibliographic Details
Published inSelecta mathematica (Basel, Switzerland) Vol. 16; no. 1; pp. 121 - 143
Main Authors Hasson, Assaf, Onshuus, Alf
Format Journal Article
LanguageEnglish
Published Basel SP Birkhäuser Verlag Basel 01.04.2010
Subjects
Mathematics
Mathematics and Statistics
14P05
03C64
03C98
03C45
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Summary:Let be a dense o-minimal structure, an unstable structure interpretable in . Then there exists X , definable in , such that X , with the induced -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.
ISSN:1022-1824
1420-9020
DOI:10.1007/s00029-010-0018-y