Logic Seminar

The question of constructing hyperdegrees with some given properties appears naturally not only in recursion theory but also in effective descriptive set theory. We are particularly concerned with the hyperdegrees, which appear in the body of some certain categories of recursive trees (Kleene trees, Spector-Gandy trees). It turns out that a compactness-type result by Kreisel is an important tool in this study. In this talk we give some applications of the latter and we conclude with an open problem.