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The Monotone Completeness Theorem in Constructive Reverse Mathematics

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Mathesis Universalis, Computability and Proof

Part of the book series: Synthese Library ((SYLI,volume 412))

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Abstract

We deal with the monotone completeness theorem in constructive reverse mathematics, and show that a weak form of the theorem is equivalent to a bounded comprehension axiom for \(\Sigma ^0_1\) formulae.

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Acknowledgements

The authors thank the Japan Society for the Promotion of Science (JSPS), Core-to-Core Program (A. Advanced Research Networks), and the first author thanks the JSPS Grant-in-Aid for Scientific Research (C) No.16K05251, for supporting the research.

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Authors and Affiliations

  1. School of Information Science, Japan Advanced Institute of Science and Technology, Nomi, Ishikawa, Japan

    Hajime Ishihara & Takako Nemoto

Authors
  1. Hajime Ishihara
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  2. Takako Nemoto
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Corresponding author

Correspondence to Hajime Ishihara .

Editor information

Editors and Affiliations

  1. Institute of Philosophy, Technical University of Berlin, Berlin, Germany

    Stefania Centrone

  2. Department of Philosophy, University of Helsinki, Helsinki, Finland

    Sara Negri

  3. University of Hamburg, Hamburg, Germany

    Deniz Sarikaya

  4. Dipartimento di Informatica, Università degli Studi di Verona, Verona, Italy

    Peter M. Schuster

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Ishihara, H., Nemoto, T. (2019). The Monotone Completeness Theorem in Constructive Reverse Mathematics. In: Centrone, S., Negri, S., Sarikaya, D., Schuster, P.M. (eds) Mathesis Universalis, Computability and Proof. Synthese Library, vol 412. Springer, Cham. https://doi.org/10.1007/978-3-030-20447-1_8

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