Intuitionistic logic and modality via topology

Abstract

In the pioneering article and two papers, written jointly with McKinsey, Tarski developed the so-called algebraic and topological frameworks for the Intuitionistic Logic and the Lewis modal system. In this paper, we present an outline of modern (non-Lewis) systems with a topological tinge. We consider topological interpretation of basic systems GL and G RZ of the provability logic in terms of the Cantor derivative and the Hausdorff residue.