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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
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
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
Linking options:
https://www.mathnet.ru/eng/im1752https://doi.org/10.1070/IM1980v015n02ABEH001252 https://www.mathnet.ru/eng/im/v43/i5/p1175
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Abstract page: | 731 | Russian version PDF: | 321 | English version PDF: | 40 | References: | 70 | First page: | 1 |
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