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Saarland University Computer Science

Categoricity Results for Second-Order ZF in Dependent Type Theory

Dominik Kirst, Gert Smolka

Interactive Theorem Proving - 8th International Conference, ITP 2017, Brasilia, Brazil, September 26-29, 2017, September 2017

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.

Link to Coq Formalisation

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