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arXiv · 1409.1336

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

Toshiyasu Arai
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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.

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Toshiyasu Arai. 2014-09-04. Lifting proof theory to the countable ordinals II: second-order indescribable cardinals. https://arxiv.org/abs/1409.1336

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