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Isolated types of finite rank: an abstract Dixmier–Moeglin equivalence

  • Omar León SánchezEmail author
  • Rahim Moosa


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 Open image in new window 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.


Model theory Totally transcendental theories Differential fields 

Mathematics Subject Classification

03C95 03C98 12H05 



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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of MathematicsUniversity of ManchesterManchesterUK
  2. 2.Department of Pure MathematicsUniversity of WaterlooWaterlooCanada

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