On antichains of spreading models of Banach spaces

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.

arXiv comment14 pages, no figures. Canadian Mathematical Bulletin (to appear)

Cited by in corpus (1)

• On the structure of the set of higher order spreading models