• Publications
• Influence
Geometric categories and o-minimal structures
• Mathematics
• 1 August 1996
The theory of subanalytic sets is an excellent tool in various analytic-geometric contexts; see, for example, Bierstone and Milman . Regrettably, certain “nice” sets—like { (x, x) : x > 0 } forExpand
Expansions of dense linear orders with the intermediate value property
• Chris Miller
• Computer Science, Mathematics
• Journal of Symbolic Logic
• 1 December 2001
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
Expansions of the Real Field with Power Functions
• Chris Miller
• Mathematics, Computer Science
• Ann. Pure Appl. Log.
• 9 June 1994
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
Expansions of o-minimal structures by sparse sets
• Mathematics
• 2001
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 theExpand
EXPONENTIATION IS HARD TO AVOID
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 polynomiallyExpand
Structures having o-minimal open core
• Mathematics
• 8 October 2009
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 denseExpand
Expansions of o-minimal structures by dense independent sets
• Mathematics, Computer Science
• Ann. Pure Appl. Log.
• 1 August 2016
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
Borel subrings of the reals
• Mathematics
• 12 June 2002
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 positiveExpand