L. Beklemishev, D. Gabelaia, “Topological completeness of the provability logic GLP”, Ann. Pure Appl. Logic, 2013, Volume 164, Issue 12,Pages <nobr>1201

This article is cited in 16 papers

Topological completeness of the provability logic GLP

L. Beklemishev^abc, D. Gabelaia^de

^a Moscow M.V. Lomonosov State University, Russian Federation
^b V.A. Steklov Mathematical Institute, RAS, Moscow, Russian Federation
^c National Research University Higher School of Economics, Russian Federation
^d TSU A. Razmadze Mathematical Institute, Tbilisi, Georgia
^e The Free University of Tbilisi, Tbilisi, Georgia

Abstract: Provability logic $\mathbf{GLP}$ is well-known to be incomplete w.r.t. Kripke semantics. A natural topological semantics of $\mathbf{GLP}$ interprets modalities as derivative operators of a polytopological space. Such spaces are called GLP-spaces whenever they satisfy all the axioms of $\mathbf{GLP}$. We develop some constructions to build nontrivial GLP-spaces and show that $\mathbf{GLP}$ is complete w.r.t. the class of all GLP-spaces.

Received: 27.11.2011
Revised: 02.12.2012
Accepted: 14.12.2012

Language: English

DOI: 10.1016/j.apal.2013.06.008