Complex cells in sharply o-minimal structures

Abstract

We extend the theory of complex cells introduced by Binyamini and Novikov to the sharply o-minimal setting, obtaining cellular preparation and parameterization theorems which are polynomially effective in the degrees of the relevant sets. Our constructions are definable, and so applying them to sets in a given reduct of R_an yields cells and cellular maps definable in the same reduct.

33 pages