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A MACHINE-ASSISTED PROOF OF GÖDEL’S INCOMPLETENESS THEOREMS FOR THE THEORY OF HEREDITARILY FINITE SETS

  • LAWRENCE C. PAULSON (a1)
Abstract
Abstract

A formalization of Gödel’s incompleteness theorems using the Isabelle proof assistant is described. This is apparently the first mechanical verification of the second incompleteness theorem. The work closely follows Świerczkowski (2003), who gave a detailed proof using hereditarily finite set theory. The adoption of this theory is generally beneficial, but it poses certain technical issues that do not arise for Peano arithmetic. The formalization itself should be useful to logicians, particularly concerning the second incompleteness theorem, where existing proofs are lacking in detail.

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*COMPUTER LABORATORY UNIVERSITY OF CAMBRIDGE CAMBRIDGE, CB3 0FD, UK E-mail: lp15@cam.ac.uk
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T Franzén . (2005). Gödel’s Theorem: An Incomplete Guide to Its Use and Abuse. Wellesley, Mass: A K Peters.

L Kirby . (2007). Addition and multiplication of sets. Mathematical Logic Quarterly,53(1), 5265.

T. Nipkow , L. C. Paulson , & M Wenzel . (2002). Isabelle/HOL: A Proof Assistant for Higher-Order Logic. Lecture Notes in Computer Science vol. 2283, Berlin: Springer.

N Shankar . (1994). Metamathematics, Machines, and Gödel’s Proof. Cambridge : Cambridge University Press.

S Świerczkowski . (2003). Finite sets and Gödel’s incompleteness theorems. Dissertationes Mathematicae, 422, 158. Available from: http://journals.impan.gov.pl/dm/Inf/422-0-1.html.

C. Urban , & C Kaliszyk . (2012). General bindings and alpha-equivalence in Nominal Isabelle. Logical Methods in Computer Science, 8(2:14), 135.

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The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
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