Expansions of algebraically closed fields in o-minimal structures

Ya'acov Peterzil, Sergei Starchenko

Research output: Contribution to journalArticlepeer-review


We develop a notion of differentiability over an algebraically closed field K of characteristic zero with respect to a maximal real closed subfield R. We work in the context of an o-minimal expansion R of the field R and obtain many of the standard results in complex analysis in this setting. In doing so we use the topological approach to complex analysis developed by Whyburn and others. We then prove a model theoretic theorem that states that the field R is definable in every proper expansion of the field K all of whose atomic relations are definable in R. One corollary of this result is the classical theorem of Chow on projective analytic sets.

Original languageEnglish
Pages (from-to)409-445
Number of pages37
JournalSelecta Mathematica, New Series
Issue number3
StatePublished - 2001

Bibliographical note

Funding Information:
The second author was partially supported by NSF


  • Compact complex manifolds
  • Nonarchimedean fields
  • o-minimal

ASJC Scopus subject areas

  • General Mathematics
  • General Physics and Astronomy


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