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

Omar León Sánchez, 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=tp(a/A) is isolated if and only if Open image in new window for every b∈acl(Aa) and q∈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.