11 Basis theorems
In earlier chapters we have seen examples of uncountable sets of reals (e.g. 
and certain 
-sets) that contain perfect subsets. In this chapter we study basis theorems for uncountable sets of reals as well as basis properties of perfect sets.
11.1 A basis theorem for 
-sets of reals
11.1.1 Friedman’s conjecture
Friedman [29] conjectured that every uncountable -set of reals has a member in each hyperdegree greater than or equal to the ...
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