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Статья

Topological completeness of the provability logic GLP

Annals of Pure and Applied Logic. 2013. Vol. 164. No. 12. P. 1201-1223.
Beklemishev L. D., Gabelaia D.

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. © 2013 Elsevier B.V.