Rybina, T. V. Undecidability of the theory of the lattice \(L^ 0_{sm}\). (English. Russian original) Zbl 0726.03031 Sib. Math. J. 31, No. 6, 1058-1059 (1990); translation from Sib. Mat. Zh. 31, No. 6(184), 215-216 (1990). The lattice \(L^ 0_{sm}\) was defined by Yu. L. Ershov [Theory of numerations (Russian) (Moscow, Nauka, 1977)]. The author proves by means of the relatively elementary definability method that the elementary theory of this lattice is hereditarily undecidable. Reviewer: A.S.Morozov (Novosibirsk) Cited in 1 Document MSC: 03D35 Undecidability and degrees of sets of sentences 03C57 Computable structure theory, computable model theory 03D45 Theory of numerations, effectively presented structures Keywords:undecidable theory PDFBibTeX XMLCite \textit{T. V. Rybina}, Sib. Math. J. 31, No. 6, 1058--1059 (1990; Zbl 0726.03031); translation from Sib. Mat. Zh. 31, No. 6(184), 215--216 (1990) Full Text: DOI References: [1] Yu. L. Ershov, Theory of Enumerations [in Russian], Nauka, Moscow (1977). [2] T. V. Rybina, ?Indecomposable elements and descending chains,? in: Abstracts of Reports, 8th All-Union Conference on Mathematical Logic, Moscow, September, 1986, Moscow (1986), p. 162. [3] Yu. L. Ershov, Decidability Problems and Constructive Models [in Russian], Nauka, Moscow (1980). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.