The proof-theoretic analysis of transfinitely iterated quasi least fixed points

Abstract

The starting point of this article is an old question asked by Feferman in his paper on Hancock’s conjecture [6] about the strength of ID₁^*. This theory is obtained from the well-known theory ID₁ by restricting fixed point induction to formulas that contain fixed point constants only positively. The techniques used to perform the proof-theoretic analysis of ID₁^* also permit to analyze its transfinitely iterated variants ID_α^*. Thus, we eventually know that |\hat{ID}_α| = |ID_α^*|.