### Cupping with random sets

**Day, A ***(University of California, Berkeley)*

Friday 06 July 2012, 14:00-15:00

Seminar Room 1, Newton Institute

#### Abstract

A set $X$ is ML-cuppable if there exists an incomplete Martin-Löf
random $R$ that joins $X$ to zero jump. It is weakly ML-cuppable if
there exists an incomplete Martin-Löf random $R$ that joins $X$
above zero jump. We prove that a set is K-trivial if and only if it is
not weakly ML-cuppable. Further, we show that a set below zero jump is
K-trivial if and only if it is not ML-cuppable. These results settle a
question of Kučera, who introduced both cuppability notions. This
is joint work with Joseph S. Miller.

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