A Machine-Assisted Proof of Gödel’s Incompleteness Theorems for the Theory of Hereditarily Finite Sets
The Review of Symbolic Logic
Cambridge University Press
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Paulson, L. (2014). A Machine-Assisted Proof of Gödel’s Incompleteness Theorems for the Theory of Hereditarily Finite Sets. The Review of Symbolic Logic, 7 484-498. https://doi.org/10.1017/S1755020314000112
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.
External DOI: https://doi.org/10.1017/S1755020314000112
This record's URL: https://www.repository.cam.ac.uk/handle/1810/245422