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Categoricity Results for Second-Order ZF in Dependent Type Theory

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Interactive Theorem Proving (ITP 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10499))

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Abstract

We formalise the axiomatic set theory second-order ZF in the constructive type theory of Coq assuming excluded middle. In this setting we prove Zermelo’s embedding theorem for models, categoricity in all cardinalities, and the correspondence of inner models and Grothendieck universes. Our results are based on an inductive definition of the cumulative hierarchy eliminating the need for ordinals and transfinite recursion.

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Authors and Affiliations

  1. Saarland University, Saarbrücken, Germany

    Dominik Kirst & Gert Smolka

Authors
  1. Dominik Kirst
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  2. Gert Smolka
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Correspondence to Dominik Kirst or Gert Smolka .

Editor information

Editors and Affiliations

  1. University of Brasília, Brasília D.F., Brazil

    Mauricio Ayala-Rincón

  2. NASA, Hampton, VA, USA

    César A. Muñoz

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Kirst, D., Smolka, G. (2017). Categoricity Results for Second-Order ZF in Dependent Type Theory. In: Ayala-Rincón, M., Muñoz, C.A. (eds) Interactive Theorem Proving. ITP 2017. Lecture Notes in Computer Science(), vol 10499. Springer, Cham. https://doi.org/10.1007/978-3-319-66107-0_20

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  • DOI: https://doi.org/10.1007/978-3-319-66107-0_20

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66106-3

  • Online ISBN: 978-3-319-66107-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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