On the modal logic of the iterated Cantor derivative and finitary operations on topological spaces

4 pages•Published: July 28, 2014

Abstract

We consider propositional language endowed with three families of modal operators:
operators of the first type are interpreted by iterations of the Cantor derivative, operators of the second and the third types are interpreted by the image and the preimage of finitary operations on a topological space. We describe logics in this language that are sound and complete w.r.t. operations of a certain kind: injective, continuous, open, closed, continuous and discrete, closed of finite rank, separately continuous and separately discrete, etc. These results are based on our recent work "On interactions of the Cantor derivative and images of finitary maps between topological spaces" (2012, submitted to Topology and its Applications).

Keyphrases: Cantor derivative, closed maps, derivational modal logic, scattered spaces

In: Nikolaos Galatos, Alexander Kurz and Constantine Tsinakis (editors). TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic, vol 25, pages 195--198

Links:	https://easychair.org/publications/paper/gVs
	https://doi.org/10.29007/th3m