The Journal of Symbolic Logic

Research Article

Lowness and nullsets

Rod Downeya1, Andre Niesa2, Rebecca Webera3 and Liang Yua4

a1 Victoria University, School of Mathematics, Statistics and Computer Science, P.O. Box 600, Wellington, New Zealand. E-mail:

a2 The University of Auckland, Department of Computer Science, Private Bag 92019, Auckland, New Zealand. E-mail:

a3 Dartmouth College, Department of Mathematics, 6188 Bradley Hall, Hanover, NH 03755, USA. E-mail:

a4 National University of Singapore, Department of Mathematics, Lower Kent Ridge Road, Singapore 117543, Singapore. E-mail:


We prove that there exists a noncomputable c.e. real which is low for weak 2-randomness, a definition of randomness due to Kurtz, and that all reals which are low for weak 2-randomness are low for Martin-Löf randomness.

(Received February 28 2006)