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# On Antichains of Spreading Models of Banach Spaces

Published:2009-12-04
Printed: Mar 2010
• Pandelis Dodos
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## Abstract

We show that for every separable Banach space $X$, either $\mathrm{SP_w}(X)$ (the set of all spreading models of $X$ generated by weakly-null sequences in $X$, modulo equivalence) is countable, or $\mathrm{SP_w}(X)$ contains an antichain of the size of the continuum. This answers a question of S.~J. Dilworth, E. Odell, and B. Sari.
 MSC Classifications: 46B20 - Geometry and structure of normed linear spaces 03E15 - Descriptive set theory [See also 28A05, 54H05]