Weakly Represented Families in Reverse Mathematics

  • Rupert Hölzl
  • Dilip Raghavan
  • Frank Stephan
  • Jing Zhang
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10010)

Abstract

We study the proof strength of various second order logic principles that make statements about families of sets and functions. Usually, families of sets or functions are represented in a uniform way by a single object. In order to be able to go beyond the limitations imposed by this approach, we introduce the concept of weakly represented families of sets and functions. This allows us to study various types of families in the context of reverse mathematics that have been studied in set theory before. The results obtained witness that the concept of weakly represented families is a useful and robust tool in reverse mathematics.

Notes

Acknowledgments

The authors would like to thank C.T. Chong, Wei Li and Yue Yang for fruitful discussions and suggestions. They are also grateful to the anonymous referee for detailed and helpful comments, in particular for pointing out a simplification of the proof of Theorem 29.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Rupert Hölzl
    • 1
  • Dilip Raghavan
    • 2
  • Frank Stephan
    • 2
    • 3
  • Jing Zhang
    • 4
  1. 1.Faculty of Computer ScienceUniversität der Bundeswehr MünchenNeubibergGermany
  2. 2.Department of MathematicsThe National University of SingaporeSingaporeRepublic of Singapore
  3. 3.Department of Computer ScienceNational University of SingaporeSingaporeRepublic of Singapore
  4. 4.Department of Mathematical SciencesCarnegie Mellon UniversityPittsburghUSA

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