 
Summary: UIC Model Theory Seminar, March 2, 2004
Kanalytic geometry over ominimal structures
(joint work with Sergei Starchenko)
Kobi Peterzil, University of Haifa
Let M be an ominimal expansion of a real closed field R, and let K be the
algebraic closure of R.
The notion of a Kholomorphic function in one and several variables, (for
Mdefinable partial functions on Kn) is defined in analogy to classical com
plex functions. Kmanifolds and Kanalytic subsets are defined similarly.
Interesting examples of such definable objects arise from algebraic geometry
and from the theory of compact complex manifolds, including its elementary
extensions.
I will discuss some of the theorems which, when interpreted over the
complex numbers, yield seemingly stronger theorems than the classical ones
(under the assumptions that the objects are definable in some ominimal
structure!).
Theorem 1. (A finiteness theorem) If M is a Kmanifold and A is a de
finable closed subset of M which is locally Kanalytic then there are finitely
many definable open sets covering A, on each of which A is the zero set of
finitely many Kholomorphic functions.
