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The Monotone Completeness Theorem in Constructive Reverse Mathematics

  • Hajime IshiharaEmail author
  • Takako Nemoto
Chapter
Part of the Synthese Library book series (SYLI, volume 412)

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.

Keywords

Constructive mathematics Reverse mathematics The monotone completeness theorem 

2010 Mathematics Subject Classification:

03F65 03B30 

Notes

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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Information ScienceJapan Advanced Institute of Science and TechnologyNomiJapan

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