Let $\mathbb{C}_{an}$ be the expansion of the structure $(\mathbb{C}; +,-,×,0,1)$ by adding the restricted complex analytic functions. This is the complex analog of the familiar $\mathbb{R}_{an}$ in O-minimality. What do we know about the model theory of $\mathbb{C}_{an}$? Model-completeness? Quantifier-elimination? etc. PS. It seems Rückert's Nullstellensatz gives us model-completeness (This came to my mind just now) Is this true?