Cupping with random sets

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• Day, A (University of California, Berkeley)
• Friday 06 July 2012, 14:00-15:00
• Seminar Room 1, Newton Institute.

If you have a question about this talk, please contact Mustapha Amrani.

Semantics and Syntax: A Legacy of Alan Turing

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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