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A Formally Verified Abstract Account of Gödel’s Incompleteness Theorems

  • Andrei PopescuEmail author
  • Dmitriy TraytelEmail author
Conference paper
First Online:
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.

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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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© 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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