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Izv. Akad. Nauk SSSR Ser. Mat., 1979, Volume 43, Issue 5, Pages 1175–1195 (Mi izv1752)  

This article is cited in 11 scientific papers (total in 11 papers)

On certain extensions of the arithmetic of addition of natural numbers

A. L. Semenov


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.

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English version:
Mathematics of the USSR-Izvestiya, 1980, 15:2, 401–418

Bibliographic databases:

UDC: 519.9
MSC: Primary 03F30; Secondary 03B25, 03C10
Received: 10.01.1979

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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\by A.~L.~Semenov
\paper On certain extensions of the arithmetic of addition of natural numbers
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1979
\vol 43
\issue 5
\pages 1175--1195
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\zmath{https://zbmath.org/?q=an:0443.03008|0417.03005}
\transl
\jour Math. USSR-Izv.
\yr 1980
\vol 15
\issue 2
\pages 401--418
\crossref{https://doi.org/10.1070/IM1980v015n02ABEH001252}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1980LD11600009}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. L. Semenov, “Logical theories of one-place functions on the set of natural numbers”, Math. USSR-Izv., 22:3 (1984), 587–618  mathnet  crossref  mathscinet  zmath
    2. Roger Villemaire, “The theory of is undecidable”, Theoretical Computer Science, 106:2 (1992), 337  crossref
    3. Jean-Eric Pin, “Logic, semigroups and automata on words”, Ann Maths Artificial Intell, 16:1 (1996), 343  crossref  mathscinet  zmath
    4. Christian Michaux, Roger Villemaire, “Presburger arithmetic and recognizability of sets of natural numbers by automata: New proofs of Cobham's and Semenov's theorems”, Annals of Pure and Applied Logic, 77:3 (1996), 251  crossref
    5. Arnaud Maes, “Morphisms and almost-periodicity”, Discrete Applied Mathematics, 86:2-3 (1998), 233  crossref
    6. Ivan Korec, “A list of arithmetical structures complete with respect to the first-order definability”, Theoretical Computer Science, 257:1-2 (2001), 115  crossref
    7. William Gasarch, G.R.. Hird, “Automata techniques for query inference machines”, Annals of Pure and Applied Logic, 117:1-3 (2002), 169  crossref
    8. S. M. Dudakov, “Collapse Result for Extensions of the Presburger Arithmetic by a Unary Function Compatible with Addition”, Math. Notes, 76:3 (2004), 339–347  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. An. A. Muchnik, Yu. L. Pritykin, A. L. Semenov, “Sequences close to periodic”, Russian Math. Surveys, 64:5 (2009), 805–871  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    10. Yu. L. Pritykin, “Almost periodicity, finite automata mappings, and related effectiveness issues”, Russian Math. (Iz. VUZ), 54:1 (2010), 59–69  mathnet  crossref  mathscinet  zmath
    11. A. S. Snyatkov, “Razreshimost teorii $\mathrm{Th}(\omega,0,1,<,+,f_0,…,f_n)$”, Model. i analiz inform. sistem, 17:3 (2010), 72–90  mathnet  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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