On Overspill Principles and Axiom Schemes for Bounded Formulas

We study the theories I∇n, L∇n and overspill principles for ∇n formulas. We show that IEn L∇n I∇n, but we do not know if I∇n L∇n. We introduce a new scheme, the growth scheme Crγ, and we prove that L∇n Cr∇n I∇n. Also, we analyse the utility of bounded collection axioms for the study of the above theories. Mathematics Subject Classification: 03F30, 03H15.