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 Tr. Mat. Inst. Steklova, 2003, Volume 242, Pages 123–135 (Mi tm410)

This article is cited in 1 scientific paper (total in 1 paper)

On Prenex Fragment of Provability Logic with Quantifiers on Proofs

R. È. Yavorskii

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We consider a fragment of provability logic with quantifiers on proofs that consists of formulas with no occurrences of quantifiers in the scope of the proof predicate. By definition, a logic ql is the set of formulas that are true in the standard model of arithmetic under every interpretation based on the standard Gödel proof predicate. We describe Kripke-style semantics for the logic ql and prove the corresponding completeness theorem. For the case of injective arithmetical interpretations, the decidability is proved.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2003, 242, 112–124

Bibliographic databases:
UDC: 510.6
Received in October 2002

Citation: R. È. Yavorskii, “On Prenex Fragment of Provability Logic with Quantifiers on Proofs”, Mathematical logic and algebra, Collected papers. Dedicated to the 100th birthday of academician Petr Sergeevich Novikov, Tr. Mat. Inst. Steklova, 242, Nauka, MAIK «Nauka/Inteperiodika», M., 2003, 123–135; Proc. Steklov Inst. Math., 242 (2003), 112–124

Citation in format AMSBIB
\Bibitem{Yav03} \by R.~\E.~Yavorskii \paper On Prenex Fragment of Provability Logic with Quantifiers on Proofs \inbook Mathematical logic and algebra \bookinfo Collected papers. Dedicated to the 100th birthday of academician Petr Sergeevich Novikov \serial Tr. Mat. Inst. Steklova \yr 2003 \vol 242 \pages 123--135 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm410} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2054490} \zmath{https://zbmath.org/?q=an:1079.03054} \transl \jour Proc. Steklov Inst. Math. \yr 2003 \vol 242 \pages 112--124 `

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This publication is cited in the following articles:
1. Yavorskiy R., “On Kripke-style semantics for the provability logic of Gödel's proof predicate with quantifiers on proofs”, J. Logic Comput., 15:4 (2005), 539–549
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