# SAS

## Seminar

### Cupping with random sets

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.#### Video

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