Recall that a subset of R is called semi-algebraic if it can be represented as a (finite) boolean combination of sets of the form {~ α ∈ R : p(~ α) = 0}, {~ α ∈ R : q(~ α) > 0} where p(~x), q(~x) are… Expand

Let $X\R^n$ be a set that is definable in an o-minimal structure over $R$. This article shows that in a suitable sense, there are very few rational points of $X$ which do not lie on some connected… Expand

The subject of o-minimality is a branch of model theory, but it has potential geometrical interest. Two excellent surveys now exist: [3] is intended for mathematical logicians while [5] is aimed at… Expand

We show that the expansion of the real field generated by the functions of a quasianalytic Denjoy-Carleman class is model complete and o-minimal, provided that the class satisfies certain closure… Expand

In the fall of 1980 the authors attended Professor Tits’ course at Yale University in which he gave an account of Gromov’s beautiful proof that every finitely generated group of polynomial growth has… Expand