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  conjectured that every uncountable -set of reals has a member in each hyperdegree greater than or equal to the ...