A generalization of Levin-Schnorr's theorem
Keita Yokoyama · arXiv (Cornell University) · 2013
In this paper, we will generalize the definition of partially random or complex reals, and then show the duality of random and complex, i.e., a generalized version of Levin-Schnorr's theorem. We also study randomness from the view point of arithmetic using the relativization to a complete $Π^0_1$-class.