  We prove three new dichotomies for Banach spaces \`a la W.T. Gowers'
dichotomies. The three dichotomies characterise respectively the spaces having
no minimal subspaces, having no subsequentially minimal basic sequences, and
having no subspaces crudely finitely representable in all of their subspaces.
We subsequently use these results to make progress on Gowers' program of
classifying Banach spaces by finding characteristic spaces present in every
space. Also, the results are used to embed any partial order of size $\aleph_1$
into the subspaces of any space without a minimal subspace ordered by
isomorphic embeddability.
