A MACHINE-ASSISTED PROOF OF GÖDEL'S INCOMPLETENESS THEOREMS FOR THE THEORY OF HEREDITARILY FINITE SETS
Accepted version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
PAULSON, LC
Abstract
A formalisation of G"odel'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 {'S}wierczkowski (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 formalisation itself should be useful to logicians, particularly concerning the second incompleteness theorem, where existing proofs are lacking in detail.
Description
Keywords
math.LO, math.LO, 68V20, 03F40
Journal Title
Review of Symbolic Logic
Conference Name
Journal ISSN
1755-0203
1755-0211
1755-0211
Volume Title
7
Publisher
Cambridge University Press (CUP)
Publisher DOI
Sponsorship
Engineering and Physical Sciences Research Council (EP/I011005/1)