User blog comment:PsiCubed2/Question: General breakdown of levels up to Second Order Arithmetic/@comment-80.98.179.160-20180208163237

ΠI-reflection: We define Πn+1 as essentially same as Πn but with 1 more oracle axioms, if n>ω, and Πn as with all oracle axioms of Πm forall m<n, if n is limit.