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arXiv · 1411.4481

An order-theoretic characterization of the Howard-Bachmann-hierarchy

Jeroen Van der Meeren·Michael Rathjen·Andreas Weiermann
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Abstract

In this article we provide an intrinsic characterization of the famous Howard-Bachmann ordinal in terms of a natural well-partial-ordering by showing that this ordinal can be realized as a maximal order type of a class of generalized trees with respect to a homeomorphic embeddability relation. We use our calculations to draw some conclusions about some corresponding subsystems of second order arithmetic. All these subsystems deal with versions of light-face $\Pi^1_1$-comprehension

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Jeroen Van der Meeren, Michael Rathjen, Andreas Weiermann. 2014-11-17. An order-theoretic characterization of the Howard-Bachmann-hierarchy. https://arxiv.org/abs/1411.4481

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