An order-theoretic characterization of the Howard-Bachmann-hierarchy
Jeroen Van der Meeren, Michael Rathjen, Andreas Weiermann · White Rose Research Online (University of Leeds, The University of Sheffield, University of York) · 2014
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 $Π^1_1$-comprehension