The provability logic of all provability predicates

2022/08/06 by Kurahashi, Taishi · 3 citations
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2208.03553

Abstract

We prove that the provability logic of all provability predicates is exactly Fitting, Marek, and Truszczyński's pure logic of necessitation N. Moreover, we introduce three extensions N4, NR, and NR4 of N and investigate the arithmetical semantics of these logics. In fact, we prove that N4, NR, and NR4 are the provability logics of all provability predicates satisfying the third condition D3 of the derivabiity conditions, all Rosser's provability predicates, and all Rosser's provability predicates satisfying D3, respectively.

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• Provability interpretation of non-normal modal logics having neighborhood semantics
• Modal logical aspects of provability predicates and consistency statements
• Refinements of provability and consistency principles for the second incompleteness theorem

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