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

Let ℜ be an expansion of a dense linear order (R, <) without endpoints having the intermediate value property, that is, for all a, b ∈ R, every continuous (parametrically) definable function f: [a, b] → R takes on all values in R between f(a) and f(b). Every expansion of the real line (ℝ, <), as well as every o-minimal expansion of (R).Expand

We show in particular that the (O-minimal) theory of the ordered field of real numbers augmented by all restricted analytic functions and all real power functions admits elimination of quantifiers and has a universal axiomatization.Expand

Given an o-minimal expansion R of the ordered additive group of real numbers and E ⊆ R, we consider the extent to which basic metric and topological properties of subsets of R definable in the… Expand

Let 3t be an O-minimal expansion of the field of real numbers. If 31 is not polynomially bounded, then the exponential function is definable (without parameters) in 32 . If 31 is polynomially… Expand

The open core of an expansion of a dense linear order is its reduct, in the sense of definability, generated by the collection of all of its open definable sets. In this paper, expansions of dense… Expand

We study the structure ( M , ( H ) H ∈ H ) of an o-minimal expansion of a densely ordered group and show that every open set definable in the structure is definably independent in M .Expand

A Borel (or even analytic) subring of R either has Hausdorff dimension 0 or is all of R. Extensions of the method of proof yield (among other things) that any analytic subring of C having positive… Expand