$K$-analytic versus ${\rm ccm}$-analytic sets in nonstandard compact complex manifolds

Volume 198 / 2008

Rahim Moosa, Sergei Starchenko Fundamenta Mathematicae 198 (2008), 139-148 MSC: Primary 03C98; Secondary 03C64, 32J27. DOI: 10.4064/fm198-2-4


It is shown that in an elementary extension of a compact complex manifold $M$, the $K$-analytic sets (where $K$ is the algebraic closure of the underlying real closed field) agree with the ccm-analytic sets if and only if $M$ is essentially saturated. In particular, this is the case for compact Kähler manifolds.


  • Rahim MoosaDepartment of Pure Mathematics
    University of Waterloo
    200 University Avenue West
    Waterloo, Ontario, Canada N2L 3G1
  • Sergei StarchenkoDepartment of Mathematics
    University of Notre Dame
    255 Hurley Hall
    Notre Dame, IN 46556-4618, U.S.A.

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