Some Set-Theoretic Reduction Principles

In this article we study several reduction principles in the context of Simpson’s set theory \(ATR_{0}^{S}\) and Kripke-Platek set theory KP (with infinity). Since \(ATR_{0}^{S}\) is the set-theoretic version of ATR0 there is a direct link to second order arithmetic and the results for reductions over \(ATR_{0}^{S}\) are as expected and more or less straightforward. However, over KP we obtain several interesting new results and are lead to some open questions.