# Topological completeness of the provability logic GLP

**Authors:** Lev D. Beklemishev, David Gabelaia  
**arXiv:** [1106.5693](https://arxiv.org/abs/1106.5693)  
**Date:** 2011-06-28  
**Summary page:** https://www.summarizepaper.com/en/paper/1106.5693v1/

## 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.