Algorithmic Randomness and Lowness Sebastiaan A. Terwijn, Domenico Zambella Abstract: We prove that there are uncountably many sets that are low for the class of Schnorr random reals. We give a purely recursion theoretic characterization of these sets and show that they all have Turing degree incomparable to 0'. This contrasts with a result of Kucera and Terwijn on sets that are low for the class of MartinĀ­Lof random reals.