Abstract
Ershov algebras, Boolean algebras, and abelian p-groups are Σ-bounded systems, and there exist universal Σ-functions in hereditarily finite admissible sets over them.
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Khisamiev A. N., “Σ-Bounded algebraic systems and universal functions. I,” Siberian Math. J., 51, No. 1, 178–192 (2010).
Ershov Yu. L., Definability and Computability [in Russian], Nauchnaya Kniga, Novosibirsk (1996).
Goncharov S. S., Countable Boolean Algebras and Decidability [in Russian], Nauchnaya Kniga, Novosibirsk (1996).
Kargapolov M. I. and Merzlyakov Yu. I., Fundamentals of the Theory of Groups, Springer-Verlag, New York, Heidelberg, and Berlin (1979).
Fuchs L., Infinite Abelian Groups. Vol. 1 [Russian translation], Mir, Moscow (1974).
Fuchs L., Infinite Abelian Groups. Vol. 2 [Russian translation], Mir, Moscow (1977).
Khisamiev A. N., “On the Ershov upper semilattice £E,” Siberian Math. J., 45, No. 1, 173–187 (2004).
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Original Russian Text Copyright © 2010 Khisamiev A. N.
The author was supported by the Russian Foundation for Basic Research (Grant 09-01-12140), the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-335.2008.1), and the President of the Russian Federation (Grant MK-3721.2007.1).
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 51, No. 3, pp. 676–693, May–June, 2010.
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Khisamiev, A.N. Σ-bounded algebraic systems and universal functions. II. Sib Math J 51, 537–551 (2010). https://doi.org/10.1007/s11202-010-0056-x
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DOI: https://doi.org/10.1007/s11202-010-0056-x