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A Formally Verified Abstract Account of Gödel’s Incompleteness Theorems

  • Andrei PopescuEmail author
  • Dmitriy TraytelEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11716)

Abstract

We present an abstract development of Gödel’s incompleteness theorems, performed with the help of the Isabelle/HOL theorem prover. We analyze sufficient conditions for the theorems’ applicability to a partially specified logic. In addition to the usual benefits of generality, our abstract perspective enables a comparison between alternative approaches from the literature. These include Rosser’s variation of the first theorem, Jeroslow’s variation of the second theorem, and the Świerczkowski–Paulson semantics-based approach. As part of our framework’s validation, we upgrade Paulson’s Isabelle proof to produce a mechanization of the second theorem that does not assume soundness in the standard model, and in fact does not rely on any notion of model or semantic interpretation.

Notes

Acknowledgments

We thank Bernd Buldt for his patient explanations on material in his monograph, and the reviewers for insightful comments and suggestions.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Computer ScienceMiddlesex UniversityLondonUK
  2. 2.Institute of Information Security, Department of Computer ScienceETH ZürichZurichSwitzerland

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