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Categoricity Results for Second-Order ZF in Dependent Type Theory

  • Dominik KirstEmail author
  • Gert SmolkaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10499)

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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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Saarland UniversitySaarbrückenGermany

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