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

Published online by Cambridge University Press:  03 April 2014

LAWRENCE C. PAULSON
LAWRENCE C. PAULSON*
Affiliation:
University of Cambridge
*
*COMPUTER LABORATORY UNIVERSITY OF CAMBRIDGE CAMBRIDGE, CB3 0FD, UK E-mail: lp15@cam.ac.uk
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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.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 7 , Issue 3 , September 2014 , pp. 484 - 498
Copyright
Copyright © Association for Symbolic Logic 2014 

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