Busy beavers gone wild

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

A note on applicability of the incompleteness theorem to human mind

AbstractWe shall present some relations between consistency and reflection principles which explain why is Gödel's incompleteness theorem wrongly used to argue that thinking machines are impossible