Definable Open Sets As Finite Unions of Definable Open Cells

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

Elementary equivalence of lattices of open sets definable in o-minimal expansions of real closed fields

It is well-known that any two real closed fields R and S are elementarily equivalent. We can then consider some simple constructions of new structures out of real closed fields, and try to determine if these constructions, when applied to R and S, give elementarily equivalent structures. We can for instance consider def(R, R), the ring of definable functions from R to R, and we obtain without d...

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 Representations of Definable C Groups

Let G be a compact affine definable C group and let r be∞ or ω. We prove that the representative definable C functions on G is dense in the space of continuous functions on G. Moreover we compare the category of compact affine definable C groups D with that of compact real algebraic groups A.