Some abstract versions of G\"odel's second incompleteness theorem based on non-classical logics
Logic
2016-02-19 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1602.05728,
title = {Some abstract versions of G\"odel's second incompleteness theorem based on non-classical logics},
author = {Lev Beklemishev and Daniyar Shamkanov},
journal= {arXiv preprint arXiv:1602.05728},
year = {2016}
}
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16 pages