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Algebra Logika, 2007, Volume 46, Number 2, Pages 217–243 (Mi al3)  

This article is cited in 7 scientific papers (total in 7 papers)

The quotient algebra of labeled forests modulo $h$-equivalence

V. L. Selivanov

Novosibirsk State Pedagogical University

Abstract: We introduce and study some natural operations on a structure of finite labeled forests, which is crucial in extending the difference hierarchy to the case of partitions. It is shown that the corresponding quotient algebra modulo the so-called $h$-equivalence is the simplest non-trivial semilattice with discrete closures. The algebra is also characterized as a free algebra in some quasivariety. Part of the results is generalized to countable labeled forests with finite chains.

Keywords: labeled forest, partition, difference hierarchy.

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English version:
Algebra and Logic, 2007, 46:2, 120–133

Bibliographic databases:

UDC: 510.532
Received: 01.03.2006
Revised: 24.01.2007

Citation: V. L. Selivanov, “The quotient algebra of labeled forests modulo $h$-equivalence”, Algebra Logika, 46:2 (2007), 217–243; Algebra and Logic, 46:2 (2007), 120–133

Citation in format AMSBIB
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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. Selivanov V.L., “Fine hierarchies and m-reducibilities in theoretical computer science”, Theoret. Comput. Sci., 405:1-2 (2008), 116–163  crossref  mathscinet  zmath  isi  elib  scopus
    2. Kudinov O.V., Selivanov V.L., Zhukov A.V., “Definability in the h-quasiorder of labeled forests”, Ann. Pure Appl. Logic, 159:3 (2009), 318–332  crossref  mathscinet  zmath  isi  elib  scopus
    3. Selivanov V.L., “Undecidability of some structures related to computation theory”, J. Logic Comput., 19:1 (2009), 177–197  crossref  mathscinet  zmath  isi  elib  scopus
    4. Selivanov V.L., “On the Wadge reducibility of $k$-partitions”, J. Log. Algebr. Program., 79:1 (2010), 92–102  crossref  mathscinet  zmath  isi  scopus
    5. A. V. Zhukov, O. V. Kudinov, V. L. Selivanov, “Definability of closure operations in the $h$-quasiorder of labeled forests”, Algebra and Logic, 49:2 (2010), 120–129  mathnet  crossref  mathscinet  zmath  isi
    6. Spreen D., “the Life and Work of Victor l. Selivanov”, Logic, Computation, Hierarchies, Ontos Mathematical Logic, 4, ed. Brattka V. Diener H. Spreen D., Walter de Gruyter Gmbh, 2014, 1–8  mathscinet  isi
    7. Selivanov V., “Towards a Descriptive Theory of Cb(0)-Spaces”, Math. Struct. Comput. Sci., 27:8 (2017), 1553–1580  crossref  mathscinet  zmath  isi  scopus
  • Алгебра и логика Algebra and Logic
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