Boris Tsirelson constructed the first Banach space that did not have a subspace isomorphic to some $\ell_p$, $1\le p < \infty$ or $c_0$. This eventually led to the Gowers-Maurey construction of hereditarily indecomposable Banach spaces. Tsirelson writes that his forcing construction was motivated by Cohen's forcing arguments:
Bill Johnson
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