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Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2013, Volume 13, Issue 2, Pages 3–14
(Mi vngu137)
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This article is cited in 5 scientific papers (total in 5 papers)
On $\Delta^0_2$-Categoricity of Boolean Algebras
N. A. Bazhenovab
a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
Abstract:
We prove that the notions of $\Delta^0_2$-categoricity and relative $\Delta^0_2$-categoricity in Boolean algebras coincide. As a corollary, we obtain that for every Turing degree $\mathbf{d}<\mathbf{0}'$ a computable Boolean algebra is $\mathbf{d}$-computably categorical if and only if it is computably categorical.
Keywords:
Boolean algebra, $\Delta^{0}_{2}$-categoricity, computable categoricity.
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UDC:
510.5+510.6+512.563
Received: 23.07.2010
Citation:
N. A. Bazhenov, “On $\Delta^0_2$-Categoricity of Boolean Algebras”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 13:2 (2013), 3–14
Citation in format AMSBIB
\Bibitem{Baz13}
\by N.~A.~Bazhenov
\paper On $\Delta^0_2$-Categoricity of Boolean Algebras
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2013
\vol 13
\issue 2
\pages 3--14
\mathnet{http://mi.mathnet.ru/vngu137}
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http://mi.mathnet.ru/eng/vngu137 http://mi.mathnet.ru/eng/vngu/v13/i2/p3
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This publication is cited in the following articles:
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N. A. Bazhenov, “D.c.e. degrees of categoricity for Boolean algebras with a distinguished automorphism”, J. Math. Sci., 211:6 (2015), 738–746
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N. A. Bazhenov, “Autostability spectra for Boolean algebras”, Algebra and Logic, 53:6 (2015), 502–505
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S. S. Goncharov, M. I. Marchuk, “Index sets of constructive models of finite and graph signatures that are autostable relative to strong constructivizations”, Algebra and Logic, 54:6 (2016), 428–439
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N. A. Bazhenov, “Degrees of autostability for linear orderings and linearly ordered Abelian groups”, Algebra and Logic, 55:4 (2016), 257–273
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N. A. Bazhenov, M. I. Marchuk, “Degrees of autostability for prime Boolean algebras”, Algebra and Logic, 57:2 (2018), 98–114
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