We give necessary and sufficient conditions on a non-oscillatory curve in an o-minimal structure such that, for any bounded definable function, there exists a definable closed set containing an initial segment of the curve on which the function is continuous. This question is translated into one on types: What are the conditions on an n-type such that, for… (More)
A proper elementary extension of a model is called small if it realizes no new types over any finite set in the base model. We answer a question of Marker, and show that it is possible to have an o-minimal structure with a maximal small extension. Our construction yields such a structure for any cardinality. We show that in some cases, notably when the base… (More)
Tracer studies are analyzed almost universally by multicompartmental models where the state variables are tracer amounts or activities in the different pools. The model parameters are rate constants, defined naturally by expressing fluxes as fractions of the source pools. We consider an alternative state space with tracer enrichments or specific activities… (More)
We prove that a function definable in an elementary extension of an o-minimal structure is bounded away from ∞ as its argument goes to ∞ by a function definable in the original structure. Moreover, this remains true if the argument is taken to approach any element of the original structure (or ±∞), and the function has limit any element of the original… (More)
Types in o-minimal theories We extend previous work on classifying o-minimal types, and develop several applications. Marker developed a dichotomy of o-minimal types into " cuts " and " noncuts, " with a further dichotomy of cuts being either " uniquely " or " non-uniquely realizable. " We use this classification to extend work by van den Dries and Miller… (More)
We consider the notion of a " stationary structure, " defined by Petrykowski in [Pet]. A structure is stationary if any function definable in an elementary extension is bounded by some function definable in the original structure. We answer a question he posed by showing that all o-minimal structures are stationary.
My research is in model theory: o-minimality, and more generally in dependent unstable theories. A theory is unstable if there is a formula that orders an infinite set of tuples in some model of the theory. A theory is independent if there is a definable binary relation on tuples and, in sufficiently saturated models, an infinite set, such that every subset… (More)