Concerning definable sets

Definable Sets in Ordered Structures

This paper introduces and begins the study of a well-behaved class of linearly ordered structures, the ^-minimal structures. The definition of this class and the corresponding class of theories, the strongly ©-minimal theories, is made in analogy with the notions from stability theory of minimal structures and strongly minimal theories. Theorems 2.1 and 2.3, respectively, provide characterizati...

Definable Sets in Valued Fields

Ind- and pro- definable sets

We describe the indand procategories of the category of definable sets, in some first order theory, in terms of points in a sufficiently saturated model.

Concerning Maximal Sets

Vapnik-chervonenkis Classes of Definable Sets

We show that a class of subsets of a structure uniformly definable by a first-order formula is a Vapnik-Chervonenkis class if and only if the formula does not have the independence property. Via this connection we obtain several new examples of Vapnik-Chervonenkis classes, including sets of positivity of finitely subanalytic functions.