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Topological completeness of the provability logic GLP

Published 28 Jun 2011 in math.LO and math.GN | (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.

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