On Antichains of Spreading Models of Banach Spaces

DOI10.4153/CMB-2010-011-1zbMATH Open1197.46009arXiv0805.2038MaRDI QIDQ5189730

Pandelis Dodos

Publication date: 11 March 2010

Published in: Canadian Mathematical Bulletin (Search for Journal in Brave)

Abstract: We show that for every separable Banach space $X$, either $spw(X)$ (the set of all spreading models of $X$ generated by weakly-null sequences in $X$, modulo equivalence) is countable, or $spw(X)$ contains an antichain of the size of the continuum. This answers a question of S. J. Dilworth, E. Odell and B. Sari.

Full work available at URL: https://arxiv.org/abs/0805.2038

zbMATH Keywords

spreading modelsquasi-ordersBorel orders\(F_\sigma\) order\(SP_w(X)\)

Mathematics Subject Classification ID

Descriptive set theory (03E15) Isomorphic theory (including renorming) of Banach spaces (46B03) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15)

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