Expansions of algebraically closed fields in o-minimal structures |
| |
Authors: | Y Peterzil S Starchenko |
| |
Institution: | (1) Department of Mathematics, University of Haifa, Haifa, Israel;(2) Department of Mathematics, University of Notre Dame, Room 370, CCMB, 46556 Notre Dame, IN, USA |
| |
Abstract: | 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. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|