English

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

Logic 2015-01-06 v2

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\Pi^1_1-comprehension

Keywords

Cite

@article{arxiv.1411.4481,
  title  = {An order-theoretic characterization of the Howard-Bachmann-hierarchy},
  author = {Jeroen Van der Meeren and Michael Rathjen and Andreas Weiermann},
  journal= {arXiv preprint arXiv:1411.4481},
  year   = {2015}
}

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46 pages