Enumerations of Turing ideals with applications (Q2277253)

A Turing ideal is a collection of sets of integers closed under Turing reducibility and join. The author studies enumerations of such objects with an eye to applications in the model theory of first and second order arithmetical systems such as \(WKL_ 0\) and \(RCA_ 0\). The techniques are Cohen and Sacks forcing, and coding techniques such as those of \textit{J. Harrison} [Thesis, Stanford 1966].