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Mat. Tr., 2005, Volume 8, Number 1, Pages 135–175 (Mi mt58)  

This article is cited in 14 scientific papers (total in 14 papers)

Variations on the Wadge Reducibility

V. L. Selivanov

A. P. Ershov Institute of Informatics Systems Sib. Br. RAS

Abstract: The Wadge reducibility in the Baire and Cantor spaces is very important in descriptive set theory. We consider the Wadge reducibility in some other topological spaces, in particular, in the $\varphi$-spaces which are topological counterparts of the algebraic directed-complete partial orderings. It turns out that the Wadge reducibility behaves worse in most spaces than in the classical case but there exist interesting examples of spaces with a better behavior as well.

Key words: Wadge reducibility, $\varphi$-space, directed-complete partial ordering, retract, Borel set, difference hierarchy.

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English version:
Siberian Advances in Mathematics, 2005, 15:3, 44–80

Bibliographic databases:

UDC: 510.225+515.126
Received: 17.03.2004

Citation: V. L. Selivanov, “Variations on the Wadge Reducibility”, Mat. Tr., 8:1 (2005), 135–175; Siberian Adv. Math., 15:3 (2005), 44–80

Citation in format AMSBIB
\Bibitem{Sel05}
\by V.~L.~Selivanov
\paper Variations on the~Wadge Reducibility
\jour Mat. Tr.
\yr 2005
\vol 8
\issue 1
\pages 135--175
\mathnet{http://mi.mathnet.ru/mt58}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1955025}
\zmath{https://zbmath.org/?q=an:1095.03042}
\transl
\jour Siberian Adv. Math.
\yr 2005
\vol 15
\issue 3
\pages 44--80


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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., “Towards a descriptive set theory for domain-like structures”, Theoret. Comput. Sci., 365:3 (2006), 258–282  crossref  mathscinet  zmath  isi  elib  scopus
    2. V. L. Selivanov, “The quotient algebra of labeled forests modulo $h$-equivalence”, Algebra and Logic, 46:2 (2007), 120–133  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    3. Selivanov V.L., “Hierarchies of $\Delta^0_2$-measurable $k$-partitions”, MLQ Math. Log. Q., 53:4-5 (2007), 446–461  crossref  mathscinet  zmath  isi  scopus
    4. Selivanov V.L., “A useful undecidable theory”, Computation and Logic in the Real World, Proceedings, Lecture Notes in Computer Science, 4497, 2007, 685–694  crossref  mathscinet  zmath  isi  scopus
    5. 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
    6. Selivanov V.L., “Undecidability in Some Structures Related to Computation Theory”, J. Logic Comput., 19:1 (2009), 177–197  crossref  mathscinet  zmath  isi  elib  scopus
    7. Selivanov V.L., “On the Wadge reducibility of $k$-partitions”, J. Log. Algebr. Program., 79:1 (2010), 92–102  crossref  mathscinet  zmath  isi  scopus
    8. Selivanov V., “Total Representations”, Log. Meth. Comput. Sci., 9:2 (2013), 05  crossref  mathscinet  isi  elib  scopus
    9. Motto Ros L., Schlicht Ph., “Lipschitz and Uniformly Continuous Reducibilities on Ultrametric Polish Spaces”, Logic, Computation, Hierarchies, Ontos Mathematical Logic, 4, eds. Brattka V., Diener H., Spreen D., Walter de Gruyter Gmbh, 2014, 213–258  mathscinet  isi
    10. Ros L.M., Schlicht Ph., Selivanov V., “Wadge-Like Reducibilities on Arbitrary Quasi-Polish Spaces”, Math. Struct. Comput. Sci., 25:8, SI (2015), 1705–1754  crossref  mathscinet  zmath  isi  scopus
    11. Schroeder M., Selivanov V., “Some Hierarchies of Qcb(0)-Spaces”, Math. Struct. Comput. Sci., 25:8, SI (2015), 1799–1823  crossref  mathscinet  zmath  isi  scopus
    12. Becher V., Grigorieff S., “Wadge Hardness in Scott Spaces and Its Effectivization”, Math. Struct. Comput. Sci., 25:7, SI (2015), 1520–1545  crossref  mathscinet  zmath  isi  elib
    13. Selivanov V., “Towards the Effective Descriptive Set Theory”, Evolving Computability, Lecture Notes in Computer Science, 9136, eds. Beckmann A., Mitrana V., Soskova M., Springer-Verlag Berlin, 2015, 324–333  crossref  mathscinet  zmath  isi  scopus
    14. Selivanov V., “Towards a Descriptive Theory of Cb(0)-Spaces”, Math. Struct. Comput. Sci., 27:8 (2017), 1553–1580  crossref  mathscinet  zmath  isi  scopus
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