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Extending Wadge Theory to k-Partitions

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Unveiling Dynamics and Complexity (CiE 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10307))

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Abstract

We extend some results about Wadge degrees of Borel subsets of Baire space to finite partitions of Baire space. A typical new result is the characterization up to isomorphism of the Wadge degrees of k-partitions with \(\mathbf {\Delta }^0_3\)-components.

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References

  1. Andretta, A.: More on Wadge determinacy. Ann. Pure Appl. Logic 144(1–3), 2–32 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  2. Andretta, A., Martin, D.A.: Borel-Wadge degrees. Fund. Math. 177(2), 175–192 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  3. Block, A.C.: Operations on a Wadge-type hierarchy of ordinal-valued functions. Masters thesis, Universiteit van Amsterdam (2014)

    Google Scholar 

  4. van Engelen, F., Miller, A., Steel, J.: Rigid Borel sets and better quasiorder theory. Contemp. Math. 65, 199–222 (1987)

    Article  MATH  Google Scholar 

  5. Hertling, P.: Topologische Komplexitätsgrade von Funktionen mit endlichem Bild. Informatik-Berichte 152, Fernuniversität Hagen (1993)

    Google Scholar 

  6. Kechris, A.S.: Classical Descriptive Set Theory. Springer, New York (1995)

    Book  MATH  Google Scholar 

  7. Kihara, T., Montalban, A.: The uniform Martin’s conjecture for many-one degrees. arXiv:1608.05065v1 [Math.LO], 17 August 2016

  8. Motto Ros, L.: Borel-amenable reducibilities for sets of reals. J. Symbolic Logic 74(1), 27–49 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Selivanov, V.L.: Hierarchies of hyperarithmetical sets and functions. Algebra Logic 22, 473–491 (1983)

    Article  MATH  Google Scholar 

  10. Selivanov, V.L.: The quotient algebra of labeled forests modulo h-equivalence. Algebra Logic 46, 120–133 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  11. Selivanov, V.L.: Hierarchies of \({\mathbf{\Delta }}^0_2\)-measurable \(k\)-partitions. Math. Logic Q. 53, 446–461 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  12. Selivanov, V.: A fine hierarchy of \(\omega \)-regular k-partitions. In: Löwe, B., Normann, D., Soskov, I., Soskova, A. (eds.) CiE 2011. LNCS, vol. 6735, pp. 260–269. Springer, Heidelberg (2011). doi:10.1007/978-3-642-21875-0_28

    Chapter  Google Scholar 

  13. Selivanov, V.L.: Fine hierarchies via Priestley duality. Ann. Pure Appl. Logic 163, 1075–1107 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  14. Selivanov, V.L.: Towards a descriptive theory of cb0-spaces. Mathematical Structures in Computer Science, September 2014. doi:10.1017/S0960129516000177. Earlier version in: arXiv:1406.3942v1 [Math.GN], 16 June 2016

  15. Van Wesep, R.: Wadge degrees and descriptive set theory. In: Kechris, A.S., Moschovakis, Y.N. (eds.) Cabal Seminar 76–77. LNM, vol. 689, pp. 151–170. Springer, Heidelberg (1978). doi:10.1007/BFb0069298

    Chapter  Google Scholar 

  16. Wadge, W.: Reducibility and determinateness in the Baire space. Ph.D. thesis, University of California, Berkely (1984)

    Google Scholar 

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Author information

Authors and Affiliations

  1. A.P. Ershov Institute of Informatics Systems SB RAS, Novosibirsk, Russia

    Victor L. Selivanov

  2. Kazan (Volga Region) Federal University, Kazan, Russia

    Victor L. Selivanov

Authors
  1. Victor L. Selivanov
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Correspondence to Victor L. Selivanov .

Editor information

Editors and Affiliations

  1. University of Turku, Turku, Finland

    Jarkko Kari

  2. Christian-Albrechts-University of Kiel, Kiel, Germany

    Florin Manea

  3. Åbo Akademi University, Turku, Finland

    Ion Petre

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Selivanov, V.L. (2017). Extending Wadge Theory to k-Partitions. In: Kari, J., Manea, F., Petre, I. (eds) Unveiling Dynamics and Complexity. CiE 2017. Lecture Notes in Computer Science(), vol 10307. Springer, Cham. https://doi.org/10.1007/978-3-319-58741-7_36

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  • DOI: https://doi.org/10.1007/978-3-319-58741-7_36

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-58740-0

  • Online ISBN: 978-3-319-58741-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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