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It is proved that a Banach space contains a subepace isomorphic to 11 if (and only if) it has a bounded sequence with no weak-Cauchy subsequence. The proof yields that a sequence of subsets of a given set has a subsequence that is either convergent or Boolean independent.A bounded sequence of elements (fn) in a Banach space B is said to be equivalent to the usual L-basis provided there is a 5 > 0 so that for all n and choices of scalars ci, ... YcnY n a Elil < I 1 Vcffill1 [1 ] Of course if (fn) has this property, then the closed linear span of the fi's is isomorphic (linearly homeomorphic) to 11. (fn) is said to be a weak-Cauchy sequence if lim b*(fn) exists for all n-4g

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