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Fundamenta Mathematicae

2002 | 172 | 2 | 153-179

Ordinal indices and Ramsey dichotomies measuring c₀-content and semibounded completeness

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Abstrakty

EN
We study the c₀-content of a seminormalized basic sequence (χₙ) in a Banach space, by the use of ordinal indices (taking values up to ω₁) that determine dichotomies at every ordinal stage, based on the Ramsey-type principle for every countable ordinal, obtained earlier by the author. We introduce two such indices, the c₀-index $ξ^{(χₙ)}₀$ and the semibounded completeness index $ξ^{(χₙ)}_b$, and we examine their relationship. The countable ordinal values that these indices can take are always of the form $ω^{ζ}$. These results extend, to the countable ordinal level, an earlier result by Odell, which was stated only for the limiting case of the first uncountable ordinal.

153-179

wydano
2002

Twórcy

autor
• Department of Mathematics, University of Athens, Panepistimiopolis, 15784 Athens, Greece