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Preprint Number 94
94. Assaf Hasson and Alf Onshuus
Minimal types in super-dependent theories
Submission date: 2 November 2007.
We give necessary and sufficient geometric conditions for a theory definable in an o-minimal structure to interpret a real closed field. The proof goes through an analysis of thorn-minimal types in super-rosy dependent theories of finite rank. We prove that such theories are coordinatised by thorn-minimal types and that such a type is unstable if an only if every non-algebraic extension thereof is. We conclude that a type is stable if and only if it admits a coordinatisation in thorn-minimal stable types. We also show that non-trivial thorn-minimal stable types extend stable sets.
Mathematics Subject Classification: 03C45; 03C64
Keywords and phrases: dependent theories, rosy theories, o-minimal theories, interpretations
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