Topological completeness of the provability logic GLP

Annals of Pure and Applied Logic 164 (12):1201-1223 (2013)

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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 are called GLP-spaces whenever they satisfy all the axioms of GLP. We develop some constructions to build nontrivial GLP-spaces and show that GLP is complete w.r.t. the class of all GLP-spaces
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DOI 10.1016/j.apal.2013.06.008
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References found in this work BETA

Provability Algebras and Proof-Theoretic Ordinals, I.Lev D. Beklemishev - 2004 - Annals of Pure and Applied Logic 128 (1-3):103-123.
Kripke Semantics for Provability Logic GLP.Lev D. Beklemishev - 2010 - Annals of Pure and Applied Logic 161 (6):756-774.
Intuitionistic Logic and Modality Via Topology.Leo Esakia - 2004 - Annals of Pure and Applied Logic 127 (1-3):155-170.
Models of Transfinite Provability Logic.David Fernández-Duque & Joost J. Joosten - 2013 - Journal of Symbolic Logic 78 (2):543-561.

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Citations of this work BETA

Models of Transfinite Provability Logic.David Fernández-Duque & Joost J. Joosten - 2013 - Journal of Symbolic Logic 78 (2):543-561.
The Polytopologies of Transfinite Provability Logic.David Fernández-Duque - 2014 - Archive for Mathematical Logic 53 (3-4):385-431.
Positive Provability Logic for Uniform Reflection Principles.Lev Beklemishev - 2014 - Annals of Pure and Applied Logic 165 (1):82-105.

View all 8 citations / Add more citations

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