Topological completeness of the provability logic GLP

Details Topological completeness of the provability logic GLP Topological completeness of the provability logic GLP

2011-06-28

arxiv.org/abs/1106.5693v1

Mathematics

Logic

Scientific paper

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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