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Seminars "Proof Theory" and "Logic Online Seminar"
October 25, 2021 18:30, Moscow, online
 


An incompleteness theorem via ordinal analysis

J. Walsh

Cornell University
Video records:
MP4 481.8 Mb

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Video files:32
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Abstract: We present an analogue of Gödel’s second incompleteness theorem. Whereas Gödel showed that sufficiently strong theories that are $\Pi^0_1$-sound and $\Sigma^0_1$-definable do not prove their own $\Pi^0_1$-soundness, we prove that sufficiently strong theories that are $\Pi^1_1$-sound and $\Sigma^1_1$-definable do not prove their own $\Pi^1_1$-soundness. Our proof does not involve the construction of a self-referential sentence but rather relies on ordinal analysis.

Language: English

Website: https://mi-ras-ru.zoom.us/j/98131048728?pwd=WnlSNGUvU3lTUTNqY0xNaWV0K0hyQT09

* Meeting identifier: 981 3104 8728 Password: 123189
 
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