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

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 use our calculations to draw some conclusions about some corresponding subsystems of second order arithmetic. All these subsystems deal with versions of light-face $$\varPi ^1_1$$ Π 1 1 -comprehension. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Mathematical Logic Springer Journals

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

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References (32)

Publisher
Springer Journals
Copyright
Copyright © 2016 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Mathematical Logic and Foundations; Mathematics, general; Algebra
ISSN
0933-5846
eISSN
1432-0665
DOI
10.1007/s00153-016-0515-6
Publisher site
See Article on Publisher Site

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 $$\varPi ^1_1$$ Π 1 1 -comprehension.

Journal

Archive for Mathematical LogicSpringer Journals

Published: Nov 5, 2016

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