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Theory of Boolean algebras with a locally finite group of automorphisms. (English. Russian original) Zbl 0633.03003

Sib. Math. J. 28, No. 3, 424-425 (1987); translation from Sib. Mat. Zh. 28, No. 3(163), 89-90 (1987).
The author defines the family F of the locally finite recursive groups such that for every \(G\in F\) the first order theory Th(K(G)) of the class of models \(K(G)=\{(B,p):\) B is a Boolean algebra, \(p\in G\) is an automorphism of \(B\}\) is heriditarily undecidable.
Reviewer: L.Esakia

MSC:

03B25 Decidability of theories and sets of sentences
03C65 Models of other mathematical theories
06E99 Boolean algebras (Boolean rings)
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References:

[1] A. Wold, ?Decidability for Boolean algebras with automorphisms,? Not. Am. Math. Soc.,22, No. 164, A-648 (1975).
[2] S. Burris, ?The first-order theory of Boolean algebras with a distinguished group of automorphisms,? Algebra Univ.,15, 156-161 (1982). · Zbl 0505.08003 · doi:10.1007/BF02483719
[3] P. F. Jurie, ?Decidabilité de la theorie èlémentaire des anneaux booléuns à operateurs dans un groups fini,? C. R. Acad. Sci. Paris, Série A,295, 215-217 (1982). · Zbl 0519.03007
[4] M. Weesw, ?Undecidable extensions of the theory of Boolean algebras,? Preprint, Humboldt Univ. Berlin, Sekt. Math., No. 89 (1984).
[5] Z. A. Dulatova, ?Extended theories of Boolean algebras,? Sib. Mat. Zh.25, No. 1, 201-204 (1984). · Zbl 0555.03003
[6] V. I. Mart’yanov, ?Undecidability of the theory of Boolean algebras with an automorphism,? Sib. Mat. Zh.,23, No. 3, 147-154 (1982).
[7] Yu. L. Ershov, Decidability Problems and Constructive Models [in Russian], Nauka, Moscow (1980).
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