Selecta Mathematica

, 7:409 | Cite as

Expansions of algebraically closed fields in o-minimal structures

  • Y. Peterzil
  • S. Starchenko


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 \( \cal {R} \) 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 \( \cal {R} \). One corollary of this result is the classical theorem of Chow on projective analytic sets.

o-minimal nonarchimedean fields compact complex manifolds 

Copyright information

© Birkhäuser Verlag, Basel 2001

Authors and Affiliations

  • Y. Peterzil
    • 1
  • S. Starchenko
    • 2
  1. 1.Department of MathematicsUniversity of HaifaHaifaIsrael
  2. 2.Department of MathematicsUniversity of Notre DameNotre DameUSA

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