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Matematicheskie Trudy, 2009, Volume 12, Number 2, Pages 170–209 (Mi mt187)  

This article is cited in 2 scientific papers (total in 2 papers)

On a semilattice of numberings

V. G. Puzarenko

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
Full-text PDF (380 kB) Citations (2)
References:
Abstract: We study some properties of a $\mathfrak c$-universal semilattice $\mathfrak A$ with the cardinality of the continuum, i.e., of an upper semilattice of $m$-degrees. In particular, it is shown that the quotient semilattice of such a semilattice modulo any countable ideal will be also $\mathfrak c$-universal. In addition, there exists an isomorphism $\imath\colon\mathfrak A\hookrightarrow\mathfrak A$ onto some ideal of the semilattice $\mathfrak A$ such that $\mathfrak A/\imath(\mathfrak A)$ will be also $\mathfrak c$-universal. Furthermore, a property of the group of its automorphisms is obtained. To study properties of this semilattice, the technique and methods of admissible sets are used. More exactly, it is shown that the semilattice $m\Sigma$-degrees $\mathrm L^{\mathbb{HF}(S)}_{m\Sigma}$ on the hereditarily finite superstructure $\mathbb{HF}(S)$ over a countable set $S$ will be a $\mathfrak c$-universal semilattice with the cardinality of the continuum.
Key words: computably enumerable set, admissible set, $\mathbb A$-numbering , $m\Sigma$-reducibility, hereditarily finite superstructure, natural ordinal, upper semilattice, a $\mathfrak c$-universal semilattice.
Received: 16.10.2008
English version:
Siberian Advances in Mathematics, 2010, Volume 20, Issue 2, Pages 128–154
DOI: https://doi.org/10.3103/S1055134410020033
Bibliographic databases:
UDC: 510.5
Language: Russian
Citation: V. G. Puzarenko, “On a semilattice of numberings”, Mat. Tr., 12:2 (2009), 170–209; Siberian Adv. Math., 20:2 (2010), 128–154
Citation in format AMSBIB
\Bibitem{Puz09}
\by V.~G.~Puzarenko
\paper On a~semilattice of numberings
\jour Mat. Tr.
\yr 2009
\vol 12
\issue 2
\pages 170--209
\mathnet{http://mi.mathnet.ru/mt187}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2599431}
\transl
\jour Siberian Adv. Math.
\yr 2010
\vol 20
\issue 2
\pages 128--154
\crossref{https://doi.org/10.3103/S1055134410020033}
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  • https://www.mathnet.ru/eng/mt187
  • https://www.mathnet.ru/eng/mt/v12/i2/p170
    Cycle of papers
    This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические труды Siberian Advances in Mathematics
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    Abstract page:390
    Full-text PDF :99
    References:67
    First page:3
     
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