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arXiv · 2203.07758

Fundamental sequences and fast-growing hierarchies for the Bachmann-Howard ordinal

David Fernández-Duque·Andreas Weiermann
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Abstract

We prove that Buchholz's system of fundamental sequences for the $\vartheta$ function enjoys various regularity conditions, including the Bachmann property. We partially extend these results to variants of the $\vartheta$ function, including a version without addition for countable ordinals. We conclude that the Hardy functions based on these notation systems enjoy natural monotonicity properties and majorize all functions defined by primitive recursion along $\vartheta(\varepsilon_{\Omega+1})$.

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David Fernández-Duque, Andreas Weiermann. 2022-03-15. Fundamental sequences and fast-growing hierarchies for the Bachmann-Howard ordinal. https://arxiv.org/abs/2203.07758

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