A Topological Completeness Theorem for Transfinite Provability Logic

2016/09/10 by Aguilera, Juan P.
#03E10 #03F45 #54G12 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1609.03074

Abstract

We prove a topological completeness theorem for the modal logic GLP containing operators ⟨λ⟩ for λ∈ Ord intended to capture progressively stronger notions of consistency in mathematical theories. We show that, given a scattered space X of large-enough rank, any sentence ϕ consistent with GLP can be satisfied in a polytopological space based on the finitely many Icard topologies over X that correspond to the finitely many modalities appearing in ϕ.

Related

• Strong Completeness of Provability Logic for Ordinal Spaces
• The polytopologies of transfinite provability logic
• Topological interpretations of provability logic
• Models of transfinite provability logic
• Periodic frames