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The Degree Spectra of Definable Relations on Boolean Algebras

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Abstract

We study some questions concerning the structure of the spectra of the sets of atoms and atomless elements in a computable Boolean algebra. We prove that if the spectrum of the set of atoms contains a 1-low degree then it contains a computable degree. We show also that in a computable Boolean algebra of characteristic (1, 1, 0) whose set of atoms is computable the spectrum of the atomless ideal consists of all Π 20 degrees.

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Authors and Affiliations

  1. Novosibirsk State University, Novosibirsk, Russia

    P. M. Semukhin

  2. University of Auckland, Auckland, New Zealand

    P. M. Semukhin

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  1. P. M. Semukhin
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Original Russian Text Copyright © 2005 Semukhin P. M.

The author was supported by the Russian Foundation for Basic Research (Grant 02-01-00593), the Leading Scientific Schools of the Russian Federation (Grant NSh-2112.2003.1), and the Program “Universities of Russia” (Grant UR.04.01.013).

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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 928–941, July–August, 2005.

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Semukhin, P.M. The Degree Spectra of Definable Relations on Boolean Algebras. Sib Math J 46, 740–750 (2005). https://doi.org/10.1007/s11202-005-0074-2

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  • DOI: https://doi.org/10.1007/s11202-005-0074-2

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