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Algebra Logika, 2007, Volume 46, Number 3, Pages 299–345 (Mi al299)  

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

The universal Lachlan semilattice without the greatest element

S. Yu. Podzorov


Abstract: We deal with some upper semilattices of $m$-degrees and of numberings of finite families. It is proved that the semilattice of all c.e. $m$-degrees, from which the greatest element is removed, is isomorphic to the semilattice of simple $m$-degrees, the semilattice of hypersimple $m$-degrees, and the semilattice of $\Sigma_2^0$-computable numberings of a finite family of $\Sigma_2^0$-sets, which contains more than one element and does not contain elements that are comparable w.r.t. inclusion.

Keywords: upper semilattice, distributive semilattice, $m$-degree, numbering, Rogers semilattice, Lachlan semilattice.

Full text: PDF file (444 kB)
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English version:
Algebra and Logic, 2007, 46:3, 163–187

Bibliographic databases:

UDC: 510.5
Received: 24.06.2006
Revised: 21.02.2007

Citation: S. Yu. Podzorov, “The universal Lachlan semilattice without the greatest element”, Algebra Logika, 46:3 (2007), 299–345; Algebra and Logic, 46:3 (2007), 163–187

Citation in format AMSBIB
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\by S.~Yu.~Podzorov
\paper The universal Lachlan semilattice without the greatest element
\jour Algebra Logika
\yr 2007
\vol 46
\issue 3
\pages 299--345
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\transl
\jour Algebra and Logic
\yr 2007
\vol 46
\issue 3
\pages 163--187
\crossref{https://doi.org/10.1007/s10469-007-0016-0}
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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, “Arithmetical $D$-degrees”, Siberian Math. J., 49:6 (2008), 1109–1123  mathnet  crossref  mathscinet  isi
    2. 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
    3. Fokina E.B., Friedman S.-D., “On S11 equivalence relations over the natural numbers”, MLQ Math Log Q, 58:1–2 (2012), 113–124  crossref  mathscinet  zmath  isi  scopus
  • Алгебра и логика Algebra and Logic
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