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Topic Archive: Goedel Incompleteness Theorems

Computational Logic SeminarTuesday, May 3, 20162:00 pmGraduate Center, rm. 4422

Lev Beklemishev

Some abstract versions of Goedel’s Second Incompleteness Theorem based on non-classical logics

Steklov Mathematical Institute of Russian Academy of Sciences in Moscow

We study abstract versions of Goedel’s second incompleteness theorem and formulate generalizations of Loeb’s derivability conditions that work for logics weaker than the classical one. We isolate the role of the contraction and weakening rules in Goedel’s theorem and give a (toy) example of a system based on modal logic without contraction invalidating Goedel’s argument. On the other hand, Goedel’s theorem is established for a version of Peano arithmetic without contraction. (Joint work with Daniyar Shamkanov)