Undecidability, incompleteness, and completeness of second-order logic in Coq

Mark Koch, Dominik Kirst

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

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 Löwenheim-Skolem theorems.

Original languageEnglish
Title of host publicationCPP 2022 - Proceedings of the 11th ACM SIGPLAN International Conference on Certified Programs and Proofs, co-located with POPL 2022
EditorsAndrei Popescu, Steve Zdancewic
PublisherAssociation for Computing Machinery, Inc
Pages274-290
Number of pages17
ISBN (Electronic)9781450391825
DOIs
StatePublished - 17 Jan 2022
Externally publishedYes
Event11th ACM SIGPLAN International Conference on Certified Programs and Proofs, CPP 2022 - co-located with POPL 2022 - Philadelphia, United States
Duration: 17 Jan 202218 Jan 2022

Publication series

NameCPP 2022 - Proceedings of the 11th ACM SIGPLAN International Conference on Certified Programs and Proofs, co-located with POPL 2022

Conference

Conference11th ACM SIGPLAN International Conference on Certified Programs and Proofs, CPP 2022 - co-located with POPL 2022
Country/TerritoryUnited States
CityPhiladelphia
Period17/01/2218/01/22

Keywords

  • completeness
  • second order logic
  • undecidability

ASJC Scopus subject areas

  • Computer Science Applications
  • Software

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