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Mathematics of the USSR-Izvestiya, 1987, Volume 29, Issue 3, Pages 477–510
DOI: https://doi.org/10.1070/IM1987v029n03ABEH000980 (Mi im1567) 		 
On arithmetic with the notion of “attainable number”

E. S. Bozhich
English version PDF (2176 kB) Russian version article
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DOI: https://doi.org/10.1070/IM1987v029n03ABEH000980
Abstract: The author investigates the extension of formal arithmetic by the proposition that a concrete “large” natural number is not attainable. It is shown in the article that although the resulting system is inconsistent, the only formulas in the language of arithmetic which can be derived by “short” proofs are those which are theorems of arithmetic.
Bibliography: 10 titles.
Received: 16.10.1984
Bibliographic databases:
UDC: 517.11
MSC: 03F20, 03F30
Language: English
Original paper language: Russian
Citation: E. S. Bozhich, “On arithmetic with the notion of “attainable number””, Math. USSR-Izv., 29:3 (1987), 477–510
Citation in format AMSBIB
\Bibitem{Boz86}
\by E.~S.~Bozhich
\paper On arithmetic with the notion of ``attainable number''
\jour Math. USSR-Izv.
\yr 1987
\vol 29
\issue 3
\pages 477--510
\mathnet{http://mi.mathnet.ru/eng/im1567}
\crossref{https://doi.org/10.1070/IM1987v029n03ABEH000980}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=883156}
\zmath{https://zbmath.org/?q=an:0645.03058|0634.03059}
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    		Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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    Abstract page:302
    Russian version PDF:101
    English version PDF:18
    References:49
    First page:1
     
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