Expansions of algebraically closed fields in o-minimal structures

• Y. Peterzil ^[1] ; S. Starchenko ^[2]
  1. [1] University of Haifa

     University of Haifa

     Israel

     
  2. [2] University of Notre Dame

     University of Notre Dame

     Township of Portage, Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 7, Nº. 3, 2001, págs. 409-445
• Idioma: inglés
• Enlaces
  • Texto completo (pdf)
• Resumen

  • 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.