An order-theoretic characterization of the Howard-Bachmann-hierarchy
Van der Meeren, J, Rathjen, M and Weiermann, A
(2017)
An order-theoretic characterization of the Howard-Bachmann-hierarchy.
Archive for Mathematical Logic, 56 (1).
pp. 79-118.
ISSN 0933-5846
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 Π₁¹-comprehension.
Metadata
Item Type:
Article
Authors/Creators:
Van der Meeren, J
Rathjen, M
Weiermann, A
Copyright, Publisher and Additional Information:
(c) 2016, Springer-Verlag Berlin Heidelberg. This is an author produced version of a paper published in the Archive for Mathematical Logic. Uploaded in accordance with the publisher's self-archiving policy. The final publication is available at Springer via https://doi.org/10.1007/s00153-016-0515-6
Keywords:
Well-partial-orderings; Kruskal’s theorem; Howard-Bachmann number; Ordinal notation systems; Natural well-orderings; Maximal order type; Collapsing function; Recursively defined trees; Tree-embeddabilities; Proof-theoretical ordinal; Impredicative theory; Independence results; Minimal bad sequence
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