RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Subscription

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Tr.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Tr., 2006, Volume 9, Number 2, Pages 109–132 (Mi mt49)  

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

Numbered Distributive Semilattices

S. Yu. Podzorov

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

Abstract: In this article, we consider several definitions of a Lachlan semilattice; i. e., a semilattice isomorphic to a principal ideal of the semilattice of computably enumerable $m$-degrees. We also answer a series of questions on constructive posets and prove that each distributive semilattice with top and bottom is a Lachlan semilattice if it admits a $\Sigma^0_3$-representation as an algebra but need not be a Lachlan semilattice if it admits a $\Sigma^0_3$-representation as a poset. The examples are constructed of distributive lattices that are constructivizable as posets but not constructivizable as join (meet) semilattices. We also prove that every locally lattice poset (in particular, every lattice and every distributive semilattice) possessing a $\Delta^0_2$-representation is positive.

Key words: distributive lattice, distributive semilattice, numbering, constructivization, positive structure, Lachlan semilattice.

Full text: PDF file (2126 kB)
References: PDF file   HTML file

English version:
Siberian Advances in Mathematics, 2007, 17:3, 171–185

Bibliographic databases:

UDC: 510.5
Received: 08.02.2006

Citation: S. Yu. Podzorov, “Numbered Distributive Semilattices”, Mat. Tr., 9:2 (2006), 109–132; Siberian Adv. Math., 17:3 (2007), 171–185

Citation in format AMSBIB
\Bibitem{Pod06}
\by S.~Yu.~Podzorov
\paper Numbered Distributive Semilattices
\jour Mat. Tr.
\yr 2006
\vol 9
\issue 2
\pages 109--132
\mathnet{http://mi.mathnet.ru/mt49}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2301601}
\transl
\jour Siberian Adv. Math.
\yr 2007
\vol 17
\issue 3
\pages 171--185
\crossref{https://doi.org/10.3103/S1055134407030029}


Linking options:
  • http://mi.mathnet.ru/eng/mt49
  • http://mi.mathnet.ru/eng/mt/v9/i2/p109

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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, “The universal Lachlan semilattice without the greatest element”, Algebra and Logic, 46:3 (2007), 163–187  mathnet  crossref  mathscinet  zmath  isi
    2. S. Yu. Podzorov, “Arithmetical $D$-degrees”, Siberian Math. J., 49:6 (2008), 1109–1123  mathnet  crossref  mathscinet  isi
    3. 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
    4. J. Wallbaum, “A $\Delta^0_2$-poset with no positive presentation”, Algebra and Logic, 51:4 (2012), 281–284  mathnet  crossref  mathscinet  zmath  isi
  • Математические труды Siberian Advances in Mathematics
    Number of views:
    This page:217
    Full text:62
    References:40
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019