O-minimal structures and real analytic geometry (Q2739385)

O-minimal structures, and in particular o-minimal expansions of the field of real numbers, are a theme of great interest not only to model theorists, but to geometers and analysts as well. The paper contains a rich, enjoyable and fascinating outline of this matter, open to experts in model theory but also in the other areas. It describes the birth and history of o-minimality and the model-theoretic framework where it originates, but, above all, it emphasizes its intriguing connections with algebraic and analytic geometry. In this perspective the author gives a wide analysis of the main o-minimal expansions of the real field, and the various ways of building them. The paper includes a list of open problems, and an exhaustive bibliography.NEWLINENEWLINEFor the entire collection see [Zbl 0963.00022].