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LOWNESS AND HIGHNESS PROPERTIES FOR RANDOMNESS NOTIONS

Given two relativizable classes R and P and a real A, we say that A is in Low(R,P) if R P A and that A is in High(R,P) if R A P. In this paper, we survey the current results on highness and lowness for Kurtz, Schnorr, recursive, Martin-Lof, and weak 2-randomness.