On the proof of Solovay's theorem

Studia Logica 50 (1):51 - 69 (1991)
Solovay's 1976 completeness result for modal provability logic employs the recursion theorem in its proof. It is shown that the uses of the recursion theorem can in this proof be replaced by the diagonalization lemma for arithmetic and that, in effect, the proof neatly fits the framework of another, enriched, system of modal logic (the so-called Rosser logic of Gauspari-Solovay, 1979) so that any arithmetical system for which this logic is sound is strong enough to carry out the proof, in particular I0+EXP. The method is adapted to obtain a similar completeness result for the Rosser logic.
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DOI 10.1007/BF00370387
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References found in this work BETA
Self-Reference and Modal Logic.George Boolos & C. Smorynski - 1988 - Journal of Symbolic Logic 53 (1):306.
Rosser Sentences.D. Guaspari & R. M. Solovay - 1979 - Annals of Mathematical Logic 16 (1):81--99.

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Citations of this work BETA
On the Provability Logic of Bounded Arithmetic.Rineke Verbrugge & Alessandro Berarducci - 1991 - Annals of Pure and Applied Logic 61 (1-2):75-93.
Interpretability Suprema in Peano Arithmetic.Paula Henk & Albert Visser - 2017 - Archive for Mathematical Logic 56 (5-6):555-584.
The Analytical Completeness of Dzhaparidze's Polymodal Logics.George Boolos - 1993 - Annals of Pure and Applied Logic 61 (1-2):95-111.

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