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

P. 15–29.
Beklemishev L. D., Shamkanov D. S.

We study abstract versions of Gödel's second incompleteness theorem and formulate generalizations of Löb's derivability conditions that work for logics weaker than the classical one. We isolate the role of contraction rule in Gödel's theorem and give a (toy) example of a system based on modal logic without contraction invalidating Gödel's argument.

Language: English
Keywords: Goedel theoremfixed pointssubstructural logics

In book

Liber Amicorum Alberti. A Tribute to Albert Visser
L.: College Publications, 2016.
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