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SUMMARY:Cupping with random sets - Day\, A (University of California\, Ber
 keley)
DTSTART:20120706T130000Z
DTEND:20120706T140000Z
UID:TALK38884@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:A set $X$ is ML-cuppable if there exists an incomplete Martin-
 L&ouml\;f\nrandom $R$ that joins $X$ to zero jump. It is weakly ML-cuppabl
 e if\nthere exists an incomplete Martin-L&ouml\;f random $R$ that joins $X
 $\nabove zero jump. We prove that a set is K-trivial if and only if it is\
 nnot weakly ML-cuppable. Further\, we show that a set below zero jump is\n
 K-trivial if and only if it is not ML-cuppable. These results settle a\nqu
 estion of Kučera\, who introduced both cuppability notions. This\nis join
 t work with Joseph S. Miller.\n
LOCATION:Seminar Room 1\, Newton Institute
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