DEFINABLE SETS IN A HYPERBOLIC GROUP

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.

DEFINABLE SETS IN ORDERED STRUCTURES. Ill

We show that any o-minimal structure has a strongly o-minimal theory. 0. Introduction. In this paper we prove that an arbitrary o-minimal structure M is strongly o-minimal. This was proved in [1] in the case when the ordering on M is dense. In §1 we show that for discrete M, o-minimal implies strongly o-minimal. This is, of course, a result on uniform finite bounds. The proof has some interesti...

Definable Sets in Ordered Structures. Ii

It is proved that any O-minimal structure M (in which the underlying order is dense) is strongly O-minimal (namely, every N elementarily equivalent to M is O-minimal). It is simultaneously proved that if M is 0minimal, then every definable set of n-tuples of M has finitely many "definably connected components." 0. Introduction. In this paper we study the structure of definable sets (of tuples) ...