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 |
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Authors/Creators: |
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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 |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 13 Oct 2016 13:53 |
Last Modified: | 05 Nov 2017 21:39 |
Published Version: | https://doi.org/10.1007/s00153-016-0515-6 |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.1007/s00153-016-0515-6 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:105924 |