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- Title
An order-theoretic characterization of the Howard-Bachmann-hierarchy.
- Authors
Van der Meeren, Jeroen; Rathjen, Michael; Weiermann, Andreas
- 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 $$\varPi ^1_1$$ -comprehension.
- Subjects
HOMEOMORPHISMS; ARITHMETIC; NUMERICAL calculations; PARTIAL algebras; MATHEMATICAL logic
- Publication
Archive for Mathematical Logic, 2017, Vol 56, Issue 1/2, p79
- ISSN
0933-5846
- Publication type
Article
- DOI
10.1007/s00153-016-0515-6