Topological completeness of the provability logic GLP
Logic
2016-02-19 v1 General Topology
Abstract
Provability logic GLP is well-known to be incomplete w.r.t. Kripke semantics. A natural topological semantics of GLP interprets modalities as derivative operators of a polytopological space. Such spaces satisfying all the axioms of GLP are called GLP-spaces. We develop some constructions to build nontrivial GLP-spaces and show that GLP is complete w.r.t. the class of all GLP-spaces.
Cite
@article{arxiv.1106.5693,
title = {Topological completeness of the provability logic GLP},
author = {Lev D. Beklemishev and David Gabelaia},
journal= {arXiv preprint arXiv:1106.5693},
year = {2016}
}