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Algebra Logika, 2004, Volume 43, Number 6, Pages 702–729 (Mi al106)  

This article is cited in 4 scientific papers (total in 4 papers)

The Computable Dimension of $I$-Trees of Infinite Height

N. T. Kogabaeva, O. V. Kudinova, R. Millerb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Cornell University

Abstract: We study computable trees with distinguished initial subtree (briefly, $I$-trees). It is proved that all $I$-trees of infinite height are computably categorical, and moreover, they all have effectively infinite computable dimension.

Keywords: computable tree with distinguished initial subtree, computable dimension, computably categorical model, branching model, effectively infinite computable dimension

Full text: PDF file (291 kB)
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English version:
Algebra and Logic, 2004, 43:6, 393–407

Bibliographic databases:

UDC: 510.53+512.562
Received: 19.02.2003
Revised: 04.06.2004

Citation: N. T. Kogabaev, O. V. Kudinov, R. Miller, “The Computable Dimension of $I$-Trees of Infinite Height”, Algebra Logika, 43:6 (2004), 702–729; Algebra and Logic, 43:6 (2004), 393–407

Citation in format AMSBIB
\Bibitem{KogKudMil04}
\by N.~T.~Kogabaev, O.~V.~Kudinov, R.~Miller
\paper The Computable Dimension of $I$-Trees of Infinite Height
\jour Algebra Logika
\yr 2004
\vol 43
\issue 6
\pages 702--729
\mathnet{http://mi.mathnet.ru/al106}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2135388}
\zmath{https://zbmath.org/?q=an:1096.03051}
\transl
\jour Algebra and Logic
\yr 2004
\vol 43
\issue 6
\pages 393--407
\crossref{https://doi.org/10.1023/B:ALLO.0000048828.44523.94}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-42249092673}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Miller R., “$d$-computable categoricity for algebraic fields”, J. Symbolic Logic, 74:4 (2009), 1325–1351  crossref  mathscinet  zmath  isi  elib  scopus
    2. A. N. Khisamiev, “Universal functions and almost $c$-simple models”, Siberian Math. J., 56:3 (2015), 526–540  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    3. Miller R., Shlapentokh A., “Computable Categoricity For Algebraic Fields With Splitting Algorithms”, Trans. Am. Math. Soc., 367:6 (2015), PII S0002-9947(2014)06093-5, 3955–3980  crossref  mathscinet  zmath  isi  elib
    4. Hirschfeldt D.R. Kramer K. Miller R. Shlapentokh A., “Categoricity Properties For Computable Algebraic Fields”, Trans. Am. Math. Soc., 367:6 (2015), PII S0002-9947(2014)06094-7, 3981–4017  crossref  mathscinet  zmath  isi  elib
  • Алгебра и логика Algebra and Logic
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