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

Tijdschriftbijdrage - Tijdschriftartikel

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 U+03A011-comprehension.
Tijdschrift: Archive for Mathematical Logic
ISSN: 0933-5846
Issue: 1-2
Volume: 56
Pagina's: 79 - 118
Jaar van publicatie:2017
Trefwoorden:Zuivere wiskunde
CSS-citation score:2
Authors from:Higher Education