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Izv. Akad. Nauk SSSR Ser. Mat., 1986, Volume 50, Issue 6, Pages 1123–1155 (Mi izv1567)  

On arithmetic with the notion of “attainable number”

E. S. Bozhich


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.

Full text: PDF file (4191 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1987, 29:3, 477–510

Bibliographic databases:

UDC: 517.11
MSC: 03F20, 03F30
Received: 16.10.1984

Citation: E. S. Bozhich, “On arithmetic with the notion of “attainable number””, Izv. Akad. Nauk SSSR Ser. Mat., 50:6 (1986), 1123–1155; 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 Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1986
\vol 50
\issue 6
\pages 1123--1155
\mathnet{http://mi.mathnet.ru/izv1567}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=883156}
\zmath{https://zbmath.org/?q=an:0645.03058|0634.03059}
\transl
\jour Math. USSR-Izv.
\yr 1987
\vol 29
\issue 3
\pages 477--510
\crossref{https://doi.org/10.1070/IM1987v029n03ABEH000980}


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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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