Abstract: We discuss applications of concepts related to randomness in
computability theory. One example is an easy way to obtain  an injury-free
solution of Post's problem, in the style of Kucera. A further one is
the class of K-trivial sets, which forms an ideal of the Turing
degrees with nice properties. The construction of a noncomputable
K-trivial set gives a further injury free solution.

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Andre Nies
Department of Computer Science, Office 565
University of Auckland
Private Bag 92019, Auckland, New Zealand
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http://www.cs.auckland.ac.nz/~nies/
+64-9-373 7599 ext.86645