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Mathematics of the USSR-Izvestiya, 1980, Volume 15, Issue 2, Pages 401–418
DOI: https://doi.org/10.1070/IM1980v015n02ABEH001252
(Mi im1752)
 

This article is cited in 22 scientific papers (total in 22 papers)

On certain extensions of the arithmetic of addition of natural numbers

A. L. Semenov
References:
Abstract: In this paper the problems of expressibility and decidability are studied for elementary theories obtained by extending the arithmetic of order and the arithmetic of addition of natural numbers. Results are obtained on the decidability and undecidability of elementary theories of concrete structures of the form $\langle\mathbf N;+,P\rangle$, where $P$ is a fixed monadic predicate, as well as results on the class of sets definable in the theory $\mathbf T\langle\mathbf N;+,\lambda x,\exists\,y\,(x=d^y)\rangle$.
Bibliography: 6 titles.
Received: 10.01.1979
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1979, Volume 43, Issue 5, Pages 1175–1195
Bibliographic databases:
UDC: 519.9
MSC: Primary 03F30; Secondary 03B25, 03C10
Language: English
Original paper language: Russian
Citation: A. L. Semenov, “On certain extensions of the arithmetic of addition of natural numbers”, Izv. Akad. Nauk SSSR Ser. Mat., 43:5 (1979), 1175–1195; Math. USSR-Izv., 15:2 (1980), 401–418
Citation in format AMSBIB
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\paper On certain extensions of the arithmetic of addition of natural numbers
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\yr 1979
\vol 43
\issue 5
\pages 1175--1195
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\transl
\jour Math. USSR-Izv.
\yr 1980
\vol 15
\issue 2
\pages 401--418
\crossref{https://doi.org/10.1070/IM1980v015n02ABEH001252}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1980LD11600009}
Linking options:
  • https://www.mathnet.ru/eng/im1752
  • https://doi.org/10.1070/IM1980v015n02ABEH001252
  • https://www.mathnet.ru/eng/im/v43/i5/p1175
  • This publication is cited in the following 22 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:731
    Russian version PDF:321
    English version PDF:40
    References:70
    First page:1
     
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