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The Halting Probability Omega: Irreducible Complexity in Pure Mathematics |
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| Authors: | Gregory Chaitin |
| Institution: | (1) IBM T. J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY, 10598, U.S.A |
| Abstract: | Some G?del centenary reflections on whether incompleteness is really serious, and whether mathematics should be done somewhat differently, based on using algorithmic complexity measured in bits of information. Enriques Lecture held on October 30, 2006 Received: November 2006 |
| Keywords: | Incompleteness uncomputability algorithmic randomness program-size complexity algorithmic complexity irreducible complexity halting problem halting probability oracle for halting problem metamathematics quasi-empirical mathematics experimental mathematics algorithmic information theory |
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