Valentini's cut-elimination for provability logic resloved

In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev, Advances in Modal Logic. CSLI Publications. pp. 67-86 (1998)
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reprint Goré, Rajeev; Ramanayake, Revantha (2012) "Valentini’s cut-elimination for provability logic resolved". Review of Symbolic Logic 5(2):212-238

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Proof Theory for Modal Logic.Sara Negri - 2011 - Philosophy Compass 6 (8):523-538.

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