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Mathematics of the USSR-Izvestiya, 1982, Volume 18, Issue 1, Pages 41–59
DOI: https://doi.org/10.1070/IM1982v018n01ABEH001382 (Mi im1547) 		 
This article is cited in 46 scientific papers (total in 46 papers)

Predicate and set-theoretic calculi based on logic without contractions

V. N. Grishin
English version PDF (950 kB) Citations (46)
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DOI: https://doi.org/10.1070/IM1982v018n01ABEH001382
Abstract: In this paper the author studies the effect of eliminating the contraction rules from the Gentzen predicate calculus, and also from set-theoretic systems based on this calculus. It turns out that the predicate calculus without contraction rules is complete relative to finite models, and eliminating contraction rules from set-theoretic systems does not change the number of derivable formulas as long as the systems contain certain natural axioms.
Bibliography: 4 titles.
Received: 14.05.1980
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1981, Volume 45, Issue 1, Pages 47–68
Bibliographic databases:
UDC: 51.01.16
MSC: Primary 03B20; Secondary 03G25
Language: English
Original paper language: Russian
Citation: V. N. Grishin, “Predicate and set-theoretic calculi based on logic without contractions”, Izv. Akad. Nauk SSSR Ser. Mat., 45:1 (1981), 47–68; Math. USSR-Izv., 18:1 (1982), 41–59
Citation in format AMSBIB
\Bibitem{Gri81}
\by V.~N.~Grishin
\paper Predicate and set-theoretic calculi based on logic without contractions
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1981
\vol 45
\issue 1
\pages 47--68
\mathnet{http://mi.mathnet.ru/im1547}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=607576}
\zmath{https://zbmath.org/?q=an:0478.03009|0464.03027}
\transl
\jour Math. USSR-Izv.
\yr 1982
\vol 18
\issue 1
\pages 41--59
\crossref{https://doi.org/10.1070/IM1982v018n01ABEH001382}
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    • This publication is cited in the following 46 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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    Abstract page:1153
    Russian version PDF:315
    English version PDF:27
    References:102
    First page:4
     
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