Immunity for Closed Sets
نویسندگان
چکیده
The notion of immune sets is extended to closed sets and Π 1 classes in particular. We construct aΠ 1 class with no computable member which is not immune. We show that for any computably inseparable sets A and B, the class S(A,B) of separating sets for A and B is immune. We show that every perfect thin Π 1 class is immune. We define the stronger notion of prompt immunity and construct an example of a Π 1 class of positive measure which is promptly immune. We show that the immune degrees in the Medvedev lattice of closed sets forms a filter. We show that for any Π 1 class P with no computable element, there is a Π 1 class Q which is not immune and has no computable element, and which is Medvedev reducible to P . We show that any random closed set is immune.
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