@inproceedings{c17a3dcd0ef9481f85ccb2252f260275,
title = "Undecidability, incompleteness, and completeness of second-order logic in Coq",
abstract = "We mechanise central metatheoretic results about second-order logic (SOL) using the Coq proof assistant. Concretely, we consider undecidability via many-one reduction from Diophantine equations (Hilbert's tenth problem), incompleteness regarding full semantics via categoricity of second-order Peano arithmetic, and completeness regarding Henkin semantics via translation to mono-sorted first-order logic (FOL). Moreover, this translation is used to transport further characteristic properties of FOL to SOL, namely the compactness and L{\"o}wenheim-Skolem theorems.",
keywords = "completeness, second order logic, undecidability",
author = "Mark Koch and Dominik Kirst",
note = "Publisher Copyright: {\textcopyright} 2022 ACM.; 11th ACM SIGPLAN International Conference on Certified Programs and Proofs, CPP 2022 - co-located with POPL 2022 ; Conference date: 17-01-2022 Through 18-01-2022",
year = "2022",
month = jan,
day = "11",
doi = "10.1145/3497775.3503684",
language = "English",
series = "CPP 2022 - Proceedings of the 11th ACM SIGPLAN International Conference on Certified Programs and Proofs, co-located with POPL 2022",
publisher = "Association for Computing Machinery, Inc",
pages = "274--290",
editor = "Andrei Popescu and Steve Zdancewic",
booktitle = "CPP 2022 - Proceedings of the 11th ACM SIGPLAN International Conference on Certified Programs and Proofs, co-located with POPL 2022",
}