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Iterative Forcing and Hyperimmunity in Reverse Mathematics

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Evolving Computability (CiE 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9136))

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Abstract

The separation between two theorems in reverse mathematics is usually done by constructing a Turing ideal satisfying a theorem P and avoiding the solutions to a fixed instance of a theorem Q. Lerman, Solomon and Towsner introduced a forcing technique for iterating a computable non-reducibility in order to separate theorems over omega-models. In this paper, we present a modularized version of their framework in terms of preservation of hyperimmunity and show that it is powerful enough to obtain the same separations results as Wang did with his notion of preservation of definitions.

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Acknowledgements

The author is thankful to Wei Wang for useful comments and discussions.

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Authors and Affiliations

  1. Laboratoire PPS, Université Paris Diderot, Paris, France

    Ludovic Patey

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  1. Ludovic Patey
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Correspondence to Ludovic Patey .

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Editors and Affiliations

  1. Department of Computer Science, Swansea University, Swansea, United Kingdom

    Arnold Beckmann

  2. University of Bucharest, Bucharest, Romania

    Victor Mitrana

  3. Sofia University, Sofia, Bulgaria

    Mariya Soskova

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Patey, L. (2015). Iterative Forcing and Hyperimmunity in Reverse Mathematics. In: Beckmann, A., Mitrana, V., Soskova, M. (eds) Evolving Computability. CiE 2015. Lecture Notes in Computer Science(), vol 9136. Springer, Cham. https://doi.org/10.1007/978-3-319-20028-6_30

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  • DOI: https://doi.org/10.1007/978-3-319-20028-6_30

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-20027-9

  • Online ISBN: 978-3-319-20028-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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