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Enumeration Reducibility and Computable Structure Theory

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Computability and Complexity

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10010))

Abstract

The relationship between enumeration degrees and abstract models of computability inspires a new direction in the field of computable structure theory. Computable structure theory uses the notions and methods of computability theory in order to find the effective contents of some mathematical problems and constructions. The paper is a survey on the computable structure theory from the point of view of enumeration reducibility.

This research was supported by Sofia university Science Fund, contract 54/12.04.2016. The second author was also supported by the L’Oréal-UNESCO program “For women in science”.

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Notes

  1. 1.

    Note, that this indexing does not quite match the usual definition of computable infinitary formulas, namely level zero in this definition corresponds to level one in the usual definition.

  2. 2.

    Theorem 17 was first announced by Soskov during his LC talk in Münster in 2002.

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  1. Faculty of Mathematics and Computer Science, Sofia University, 5 James Bourchier Blvd, 1164, Sofia, Bulgaria

    Alexandra A. Soskova & Mariya I. Soskova

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  1. Alexandra A. Soskova
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  2. Mariya I. Soskova
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Correspondence to Mariya I. Soskova .

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  1. Victoria University of Wellington, Wellington, New Zealand

    Adam Day

  2. University of Bergen, Bergen, Norway

    Michael Fellows

  3. Victoria University of Wellington, Wellington, New Zealand

    Noam Greenberg

  4. University of Auckland, Auckland, New Zealand

    Bakhadyr Khoussainov

  5. Massey University, Auckland, New Zealand

    Alexander Melnikov

  6. University of Bergen, Bergen, Norway

    Frances Rosamond

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Soskova, A.A., Soskova, M.I. (2017). Enumeration Reducibility and Computable Structure Theory. In: Day, A., Fellows, M., Greenberg, N., Khoussainov, B., Melnikov, A., Rosamond, F. (eds) Computability and Complexity. Lecture Notes in Computer Science(), vol 10010. Springer, Cham. https://doi.org/10.1007/978-3-319-50062-1_19

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