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Izv. Akad. Nauk SSSR Ser. Mat., 1989, Volume 53, Issue 5, Pages 915–943 (Mi izv1282)  

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

On the classification of propositional provability logics

L. D. Beklemishev


Abstract: The general notion of a modal propositional provability logic was introduced by S. N. Artëmov (1979) and A. Visser (1984). In this paper it is proved that the four infinite series of provability logics known at the present time – $\operatorname{GL}_\alpha$, $\operatorname{GL}_\beta^-$, $S_\beta$, and $D_\beta$ ($\alpha,\beta\subseteq\omega$, $\omega\setminus\beta$ finite) – include all such logics.
Bibliography: 14 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1990, 35:2, 247–275

Bibliographic databases:

UDC: 512
MSC: Primary 03B45; Secondary 03F30
Received: 13.12.1988

Citation: L. D. Beklemishev, “On the classification of propositional provability logics”, Izv. Akad. Nauk SSSR Ser. Mat., 53:5 (1989), 915–943; Math. USSR-Izv., 35:2 (1990), 247–275

Citation in format AMSBIB
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\by L.~D.~Beklemishev
\paper On the classification of propositional provability logics
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1989
\vol 53
\issue 5
\pages 915--943
\mathnet{http://mi.mathnet.ru/izv1282}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1024449}
\zmath{https://zbmath.org/?q=an:0704.03005}
\transl
\jour Math. USSR-Izv.
\yr 1990
\vol 35
\issue 2
\pages 247--275
\crossref{https://doi.org/10.1070/IM1990v035n02ABEH000701}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1989EF86000001}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. R. È. Yavorskii, “On Prenex Fragment of Provability Logic with Quantifiers on Proofs”, Proc. Steklov Inst. Math., 242 (2003), 112–124  mathnet  mathscinet  zmath
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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