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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)

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