We prove that every uncountable hyperarithmetic set has a member of each hyperdegree > 0, the hyperdegree of Kleene's 0. We improve the main result of Friedman [1] by proving his conjecture that every uncountable hyperarithmetic set has a member of each hyperdegree > 0, the hyperdegree of Kleene's 0. This result has been obtained independently by Friedman by a different method. Friedman's proof uses ideas employed by L. Harrington to obtain a partial result. In [2] it is shown that there is a… Expand