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Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2012, Volume 12, Issue 3, Pages 35–45 (Mi vngu4)  

This article is cited in 3 scientific papers (total in 3 papers)

Hyperarithmetical Categoricity of the Boolean Algebra $\mathfrak{B}(\omega^{\alpha}\times\eta)$

N. A. Bazhenov

Novosibirsk State University

Abstract: We consider $\Delta^{0}_{\beta}$-categoricity in Boolean algebras. We prove the following theorem: if $\delta$ is a limit ordinal or 0, $n\in\omega$, and $\delta+n\geqslant 1$, then the Boolean algebra $\mathfrak{B}(\omega^{\delta+n}\times\eta)$ is $\Delta^{0}_{\delta+2n+1}$-categorical and not $\Delta^{0}_{\delta+2n}$-categorical.

Keywords: Boolean algebra, categoricity, back-and-forth relations.

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English version:
Journal of Mathematical Sciences, 2014, 202:1, 40–49

UDC: 510.5+510.6+512.563
Received: 05.01.2010

Citation: N. A. Bazhenov, “Hyperarithmetical Categoricity of the Boolean Algebra $\mathfrak{B}(\omega^{\alpha}\times\eta)$”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 12:3 (2012), 35–45; J. Math. Sci., 202:1 (2014), 40–49

Citation in format AMSBIB
\Bibitem{Baz12}
\by N.~A.~Bazhenov
\paper Hyperarithmetical Categoricity of the Boolean Algebra $\mathfrak{B}(\omega^{\alpha}\times\eta)$
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2012
\vol 12
\issue 3
\pages 35--45
\mathnet{http://mi.mathnet.ru/vngu4}
\transl
\jour J. Math. Sci.
\yr 2014
\vol 202
\issue 1
\pages 40--49
\crossref{https://doi.org/10.1007/s10958-014-2032-7}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. A. Bazhenov, “O $\Delta^0_2$-kategorichnosti bulevykh algebr”, Vestn. NGU. Ser. matem., mekh., inform., 13:2 (2013), 3–14  mathnet
    2. S. S. Goncharov, M. I. Marchuk, “Indeksnye mnozhestva avtoustoichivykh otnositelno silnykh konstruktivizatsii konstruktivnykh modelei konechnoi signatury i signatury grafov”, Algebra i logika, 54:6 (2015), 663–679  mathnet  crossref  mathscinet; 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  crossref  isi
    3. N. A. Bazhenov, “Degrees of autostability relative to strong constructivizations for Boolean algebras”, Algebra and Logic, 55:2 (2016), 87–102  mathnet  crossref  crossref  isi
  • Вестник Новосибирского государственного университета. Серия: математика, механика, информатика
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