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

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 us...

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Bibliographic Details
Published in:arXiv.org 2015-01
Main Authors: Jeroen Van der Meeren, Rathjen, Michael, Weiermann, Andreas
Format: Article
Language:English
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Summary: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
ISSN:2331-8422