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Algebra Logika, 2005, Volume 44, Number 2, Pages 148–172 (Mi al99)  

This article is cited in 11 scientific papers (total in 11 papers)

Local Structure of Rogers Semilattices of $\Sigma^0_n$-Computable Numberings

S. Yu. Podzorov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We deal in specific features of the algebraic structure of Rogers semilattices of $\Sigma^0_n$ – computable numberings, for $n\geqslant2$. It is proved that any Lachlan semilattice is embeddable (as an ideal) in such every semilattice, and that over an arbitrary non $0'$-principal element of such a lattice, any Lachlan semilattice is embeddable (as an interval) in it.

Keywords: Rogers semilattice, Lachlan semilattice, $\Sigma^0_n$-computable numbering

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English version:
Algebra and Logic, 2005, 44:1, 82–94

Bibliographic databases:

UDC: 510.5
Received: 23.04.2004

Citation: S. Yu. Podzorov, “Local Structure of Rogers Semilattices of $\Sigma^0_n$-Computable Numberings”, Algebra Logika, 44:2 (2005), 148–172; Algebra and Logic, 44:1 (2005), 82–94

Citation in format AMSBIB
\Bibitem{Pod05}
\by S.~Yu.~Podzorov
\paper Local Structure of Rogers Semilattices of~$\Sigma^0_n$-Computable Numberings
\jour Algebra Logika
\yr 2005
\vol 44
\issue 2
\pages 148--172
\mathnet{http://mi.mathnet.ru/al99}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2170694}
\zmath{https://zbmath.org/?q=an:1104.03038}
\transl
\jour Algebra and Logic
\yr 2005
\vol 44
\issue 1
\pages 82--94
\crossref{https://doi.org/10.1007/s10469-005-0010-3}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-18244400091}


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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. S. Yu. Podzorov, “Dual Covers of the Greatest Element of the Rogers Semilattice”, Siberian Adv. Math., 15:2 (2005), 104–114  mathnet  mathscinet  zmath
    2. S. Yu. Podzorov, “Numbered Distributive Semilattices”, Siberian Adv. Math., 17:3 (2007), 171–185  mathnet  crossref  mathscinet
    3. S. Yu. Podzorov, “On the definition of a Lachlan semilattice”, Siberian Math. J., 47:2 (2006), 315–323  mathnet  crossref  mathscinet  zmath  isi
    4. S. Yu. Podzorov, “The universal Lachlan semilattice without the greatest element”, Algebra and Logic, 46:3 (2007), 163–187  mathnet  crossref  mathscinet  zmath  isi
    5. S. Yu. Podzorov, “Arithmetical $D$-degrees”, Siberian Math. J., 49:6 (2008), 1109–1123  mathnet  crossref  mathscinet  isi
    6. Podzorov S., “Upper semilattices in many-one degrees”, Logic and Theory of Algorithms, Lecture Notes in Computer Science, 5028, 2008, 491–497  crossref  mathscinet  zmath  isi  scopus
    7. S. A. Badaev, S. S. Goncharov, “Generalized computable universal numberings”, Algebra and Logic, 53:5 (2014), 355–364  mathnet  crossref  mathscinet  isi
    8. S. S. Ospichev, “Computable families of sets in Ershov hierarchy without principal numberings”, J. Math. Sci., 215:4 (2016), 529–536  mathnet  crossref
    9. M. Kh. Faizrahmanov, “The Rogers semilattices of generalized computable enumerations”, Siberian Math. J., 58:6 (2017), 1104–1110  mathnet  crossref  crossref  isi  elib
    10. S. A. Badaev, A. A. Issakhov, “Some absolute properties of $A$-computable numberings”, Algebra and Logic, 57:4 (2018), 275–288  mathnet  crossref  crossref  isi
    11. S. S. Ospichev, “Fridbergovy numeratsii semeistv chastichno vychislimykh funktsionalov”, Sib. elektron. matem. izv., 16 (2019), 331–339  mathnet  crossref
  • Алгебра и логика Algebra and Logic
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