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Cupping with random sets

Presented by: 
A Day University of California, Berkeley
Date: 
Friday 6th July 2012 - 14:00 to 15:00
Venue: 
INI Seminar Room 1
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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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons