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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm198-2-4,
author = {Rahim Moosa and Sergei Starchenko},
title = {K-analytic versus ccm-analytic sets in nonstandard compact complex manifolds},
journal = {Fundamenta Mathematicae},
volume = {201},
year = {2008},
pages = {139-148},
zbl = {1147.03022},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm198-2-4}
}
Rahim Moosa; Sergei Starchenko. K-analytic versus ccm-analytic sets in nonstandard compact complex manifolds. Fundamenta Mathematicae, Tome 201 (2008) pp. 139-148. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm198-2-4/