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 -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}
}
Comments
46 pages