Iterating the recursively Mahlo operations

Toshiyasu Arai

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arXiv · 1005.1987

Iterating the recursively Mahlo operations

Toshiyasu Arai

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Abstract

In this paper we address a problem: How far can we iterate lower recursively Mahlo operations in higher reflecting universes? Or formally: How much can lower recursively Mahlo operations be iterated in set theories for higher reflecting universes? It turns out that in $Π_N$-reflecting universes the lowest recursively Mahlo operation can be iterated along towers of $Σ_1$-exponential orderings of height $N-3$, and that all we can do is such iterations. Namely the set theory for $Π_N$-reflecting universes is proof-theoretically reducible to iterations of the operation along such a tower.

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BibTeX RIS

Toshiyasu Arai. 2010-05-12. Iterating the recursively Mahlo operations. https://arxiv.org/abs/1005.1987

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