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Complexity of some natural problems on the class of computable I-algebras

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Abstract

We study computable Boolean algebras with distinguished ideals (I-algebras for short). We prove that the isomorphism problem for computable I-algebras is Σ 11 -complete and show that the computable isomorphism problem and the computable categoricity problem for computable I-algebras are Σ 03 -complete.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    N. T. Kogabaev

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  1. N. T. Kogabaev
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Original Russian Text Copyright © 2006 Kogabaev N. T.

The author was partially supported by the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-2112.2003.1), the Russian Foundation for Basic Research (Grant 05-01-00819), and the Program “Universities of Russia” (Grant UR.04.01.198).

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Translated from Sibirski \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Matematicheski \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Zhurnal, Vol. 47, No. 2, pp. 352–360, March–April, 2006.

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Kogabaev, N.T. Complexity of some natural problems on the class of computable I-algebras. Sib Math J 47, 291–297 (2006). https://doi.org/10.1007/s11202-006-0041-6

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  • DOI: https://doi.org/10.1007/s11202-006-0041-6

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