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Recursion Theory by Liang Yu, Chi Tat Chong

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11 Basis theorems

In earlier chapters we have seen examples of uncountable sets of reals (e.g. image and certain image-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 image-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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