Model Theory of Topological Structures

Abstract

This article will survey some of the developments in topological model theory of the last ten years, that means since the appearence of the monograph [Flum-Ziegler 1980]. In particular we shall try to give a uniform treatment of results obtained in the model theory of topological spaces: they show the role of topological notions like relative compactness, Cantor’s derivative, scatteredness, ... in topological model theory. To make this survey article as self-contained as possible we start with a review of the main concepts and results of topological model theory (cf. [Flum-Ziegler 1980] for a detailed presentation and [Ziegler 1985] for a survey article).