Cupping with random sets
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If you have a question about this talk, please contact Mustapha Amrani.
Semantics and Syntax: A Legacy of Alan Turing
A set $X$ is MLcuppable if there exists an incomplete MartinLöf
random $R$ that joins $X$ to zero jump. It is weakly MLcuppable if
there exists an incomplete MartinLöf random $R$ that joins $X$
above zero jump. We prove that a set is Ktrivial if and only if it is
not weakly MLcuppable. Further, we show that a set below zero jump is
Ktrivial if and only if it is not MLcuppable. 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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