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Boolean algebras of elementary characteristic (1, 0, 1) whose set of atoms and Ershov–Tarski ideal are computable

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Algebra and Logic Aims and scope

It is proved that there exists a computable Boolean algebra of elementary characteristics (1, 0, 1) which has a computable set of atoms and a computable Ershov–Tarski ideal, but no strongly computable isomorphic copy. Also a description of \( \Delta_6^0 \)-computable Boolean algebras is presented.

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Authors and Affiliations

  1. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    M. N. Leontieva

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  1. M. N. Leontieva
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Correspondence to M. N. Leontieva.

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Supported by the RFBR (project No. 11-01-00236), by the Grants Council (under RF President) for State Aid of Leading Scientific Schools (grant NSh-3606.2010.1), by the Grants Council (under RF President) for State Aid of Young Doctors of Science (project MD-3377.2008.1), and by the Federal Program “Scientific and Scientific-Pedagogical Cadres for Innovative Russia” in 2009–2013 (gov. contract No. 02.740.11.0429).

Translated from Algebra i Logika, Vol. 50, No. 2, pp. 133–151, March-April, 2011.

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Leontieva, M.N. Boolean algebras of elementary characteristic (1, 0, 1) whose set of atoms and Ershov–Tarski ideal are computable. Algebra Logic 50, 93–105 (2011). https://doi.org/10.1007/s10469-011-9126-9

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  • DOI: https://doi.org/10.1007/s10469-011-9126-9

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