Lifting proof theory to the countable ordinals II: second-order indescribable cardinals

Abstract

We show that the existence of a Pi^{1}_{N}-indescribable cardinal over the Zermelo-Fraenkel's set theory ZF is proof-theoretically reducible to iterations of Mostowski collapsings and lower Mahlo operations. Furthermore we describe a proof-theoretic bound on definable countable ordinals whose existence is provable from the existence of second order indescribable cardinals over ZF.

arXiv admin note: text overlap with arXiv:1111.0462

References in corpus (1)

• Iterating the recursively Mahlo operations