TAMING THE ‘ELSEWHERE’: ON EXPRESSIVITY OF TOPOLOGICAL LANGUAGES

Abstract In topological modal logic, it is well known that the Cantor derivative more expressive than closure, and ‘elsewhere’, or ‘difference’, operator ‘somewhere’ operator. 2014, Kudinov Shehtman asked whether combination of closure elsewhere becomes strictly when adding derivative. this paper we give an affirmative answer: in fact, alone can define properties spaces not expressible with elsewhere. To prove this, develop a novel theory morphisms which preserve formulas