Some abstract versions of Gödel's second incompleteness theorem based on non-classical logics [article]

Lev Beklemishev, Daniyar Shamkanov
2016 arXiv   pre-print
We study abstract versions of G\"odel's second incompleteness theorem and formulate generalizations of L\"ob's derivability conditions that work for logics weaker than the classical one. We isolate the role of contraction rule in G\"odel's theorem and give a (toy) example of a system based on modal logic without contraction invalidating G\"odel's argument.
arXiv:1602.05728v1 fatcat:tkoejgtcx5gwrcnhd6jvewjc5e