Complex analytic geometry in nonstandard setting

Kobi Peterzil, Sergei Starchenko

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


Given an arbitrary o-minimal expansion of a real closed field R, we
develop the basic theory of definable manifolds and definable analytic sets, with
respect to the algebraic closure of R, along the lines of classical complex analytic
geometry. Because of the o-minimality assumption, we obtain strong theorems on
removal of singularities and strong finiteness results in both the classical and the
nonstandard settings.
We also use a theorem of Bianconi to characterize all complex analytic sets
definable in Rexp.
Original languageEnglish
Title of host publicationModel Theory with Applications to Algebra and Analysis
EditorsZ. Chatzidakis , D. Macpherson , A. Pillay , A. Wilkie
StatePublished - 2008


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