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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.

MSC:

03D35 Undecidability and degrees of sets of sentences
03C57 Computable structure theory, computable model theory
03D45 Theory of numerations, effectively presented structures
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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).
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