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Algebra Logika, 2004, Volume 43, Number 4, Pages 425–444 (Mi al81)  

This article is cited in 13 scientific papers (total in 13 papers)

Difference Hierarchy in $\varphi$-Spaces

V. L. Selivanov

Novosibirsk State Pedagogical University

Abstract: Some results on the Borel and difference hierarchies of subsets in $\varphi$-spaces are established. For instance, we prove analogs of the Hausdorff theorem (relating the difference and Borel hierarchies) and the Lavrentyev theorem (asserting the non-collapse of the difference hierarchy).

Keywords: $\varphi$-space, Borel hierarchy, difference hierarchy

Full text: PDF file (227 kB)
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English version:
Algebra and Logic, 2004, 43:3, 238–248

Bibliographic databases:

UDC: 510.532
Received: 22.04.2003
Revised: 04.02.2004

Citation: V. L. Selivanov, “Difference Hierarchy in $\varphi$-Spaces”, Algebra Logika, 43:4 (2004), 425–444; Algebra and Logic, 43:3 (2004), 238–248

Citation in format AMSBIB
\Bibitem{Sel04}
\by V.~L.~Selivanov
\paper Difference Hierarchy in $\varphi$-Spaces
\jour Algebra Logika
\yr 2004
\vol 43
\issue 4
\pages 425--444
\mathnet{http://mi.mathnet.ru/al81}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2105847}
\zmath{https://zbmath.org/?q=an:1062.03042}
\transl
\jour Algebra and Logic
\yr 2004
\vol 43
\issue 3
\pages 238--248
\crossref{https://doi.org/10.1023/B:ALLO.0000035115.44324.5d}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33750048966}


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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. V. L. Selivanov, “Classifying Countable Boolean Terms”, Algebra and Logic, 44:2 (2005), 95–108  mathnet  crossref  mathscinet  zmath
    2. V. L. Selivanov, “Variations on the Wadge Reducibility”, Siberian Adv. Math., 15:3 (2005), 44–80  mathnet  mathscinet  zmath
    3. 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
    4. de Brecht M., “Quasi-Polish Spaces”, Ann. Pure Appl. Log., 164:3 (2013), 356–381  crossref  mathscinet  zmath  isi  scopus
    5. 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
    6. de Brecht M., “Levels of Discontinuity, Limit-Computability, and Jump Operators”, Logic, Computation, Hierarchies, Ontos Mathematical Logic, 4, eds. Brattka V., Diener H., Spreen D., Walter de Gruyter Gmbh, 2014, 79–107  mathscinet  isi
    7. 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
    8. 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
    9. Pauly A., de Brecht M., “Descriptive Set Theory in the Category of Represented Spaces”, 2015 30Th Annual Acm/IEEE Symposium on Logic in Computer Science (Lics), IEEE Symposium on Logic in Computer Science, IEEE, 2015, 438–449  crossref  mathscinet  zmath  isi  scopus
    10. Selivanov V., “Towards a Descriptive Theory of Cb(0)-Spaces”, Math. Struct. Comput. Sci., 27:8 (2017), 1553–1580  crossref  mathscinet  zmath  isi  scopus
    11. Camerlo R., “Continuous Reducibility: Functions Versus Relations”, Rep. Math. Log., 54 (2019), 45–63  crossref  mathscinet  zmath  isi  scopus
    12. de Brecht M., Pauly A., Schroeder M., “Overt Choice”, Computability, 9:3-4 (2020), 169–191  crossref  mathscinet  zmath  isi  scopus
    13. Callard A., Hoyrup M., “Descriptive Complexity on Non-Polish Spaces”, Leibniz International Proceedings in Informatics, 154, eds. Paul C., Blaser M., Schloss Dagstuhl, Leibniz Center Informatics, 2020, 8  crossref  mathscinet  isi  scopus
  • Алгебра и логика Algebra and Logic
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