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Preprint Number 1345
1345. Omar León Sánchez and Rahim Moosa A note on isolated types of finite rank E-mail: , Submission date: 4 December 2017 Abstract: Suppose T is totally transcendental and every minimal non-locally-modular type is nonorthogonal to a nonisolated minimal type over the empty set. It is shown that a finite rank type p=tp(a/A) is isolated if and only if a is independent from q(U) over Ab for every b in acl(Aa) and q in S(Ab) nonisolated and minimal. This applies to the theory of differentially closed fields -- where it is motivated by the differential Dixmier-Moeglin equivalence problem -- and the theory of compact complex manifolds. Mathematics Subject Classification: 03C95, 03C98, 12H05 Keywords and phrases: model theory totally transcendental theories, differential fields |

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