An Approach to the Dimension Theory of Continous Geometry from the Standpoint of Boolean Valued Analysis

Abstract

Recently Boolean valued analysis (i.e., analysis based on Boolean valued set theory) has been extensively studied by G. Takeuti [14-16]. The main purpose of this paper is to show, by using this technique, that any continuous geometry can be viewed as an irreducible continuous geometry in its center valued set theory. This makes the transition from irreducible continuous geometries to reducible ones automatic.