A family is constructed of cardinality equal to the continuum, whose members are totally incomparable hereditarily indecomposable Banach spaces.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm151-3-6, author = {I. Gasparis}, title = {A continuum of totally incomparable hereditarily indecomposable Banach spaces}, journal = {Studia Mathematica}, volume = {151}, year = {2002}, pages = {277-298}, zbl = {1004.46005}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm151-3-6} }
I. Gasparis. A continuum of totally incomparable hereditarily indecomposable Banach spaces. Studia Mathematica, Tome 151 (2002) pp. 277-298. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm151-3-6/