Abstract
Suppose T is a totally transcendental first-order theory 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 \(p={\text {tp}}(a/A)\) is isolated if and only if 
for every \(b\in {\text {acl}}(Aa)\) 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.
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Acknowledgements: R. Moosa was partially supported by an NSERC Discovery Grant.
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León Sánchez, O., Moosa, R. Isolated types of finite rank: an abstract Dixmier–Moeglin equivalence. Sel. Math. New Ser. 25, 10 (2019). https://doi.org/10.1007/s00029-019-0450-6
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DOI: https://doi.org/10.1007/s00029-019-0450-6