Busy beavers gone wild

Published 17 Jun 2009 in cs.LO | (0906.3257v1)

Abstract: We show some incompleteness results a la Chaitin using the busy beaver functions. Then, with the help of ordinal logics, we show how to obtain a theory in which the values of the busy beaver functions can be provably established and use this to reveal a structure on the provability of the values of these functions.

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