@inproceedings{e30604305cec4815962b20cc1f36abbb,
title = "The generalised continuum hypothesis implies the axiom of choice in Coq",
abstract = "We discuss and compare two Coq mechanisations of Sierpinski's result that the generalised continuum hypothesis (GCH) implies the axiom of choice (AC). The first version shows the result, originally stated in first-order ZF set-theory, for a higher-order set theory convenient to work with in Coq. The second version presents a corresponding theorem for Coq's type theory itself, concerning type-theoretic formulations of GCH and AC. Both versions rely on the classical law of excluded middle and extensionality assumptions but we localise the use of axioms where possible.",
keywords = "Coq, axiom of choice, dependent type theory, generalised continuum hypothesis, higher-order set theory",
author = "Dominik Kirst and Felix Rech",
note = "Publisher Copyright: {\textcopyright} 2021 ACM.; 10th ACM SIGPLAN International Conference on Certified Programs and Proofs, CPP 2021, co-located with POPL 2021 ; Conference date: 17-01-2021 Through 19-01-2021",
year = "2021",
month = jan,
day = "20",
doi = "10.1145/3437992.3439932",
language = "English",
series = "CPP 2021 - Proceedings of the 10th ACM SIGPLAN International Conference on Certified Programs and Proofs, co-located with POPL 2021",
publisher = "Association for Computing Machinery, Inc",
pages = "313--326",
editor = "Catalin Hritcu and Andrei Popescu",
booktitle = "CPP 2021 - Proceedings of the 10th ACM SIGPLAN International Conference on Certified Programs and Proofs, co-located with POPL 2021",
}