The theory of subanalytic sets is an excellent tool in various analytic-geometric contexts; see, for example, Bierstone and Milman [1]. Regrettably, certain “nice” sets—like { (x, x) : x > 0 } for… Expand

The structure of definable sets and maps in dense elementary pairs of o-minimal expansions of ordered abelian groups is described. It turns out that a certain notion of “small definable set” plays a… Expand

Publisher Summary The chapter presents the elementary theory of the structure (R , + , .), and the results could be extended to the structure (R, +, ., exp). Some aspects of on (R , + , .) are… Expand

This article points out some remarkable facts implicit in the results of Lojasiewicz [LI] and Gabrielov [Ga]. An important consequence of Tarski's work [T] on the elementary theory of the reals is a… Expand

numbers with exponentiation is model complete. When we combine this with Hovanskii's finiteness theorem [9], it follows that the real exponential field is o-minimal. In o-minimal expansions of the… Expand