For every uncountable regular cardinal κ, every κ-Borel partition of the space of all members of whose enumerating function does not have fixed points has a homogeneous club.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm177-2-3, author = {David Asper\'o}, title = {On simple partitions of $[$\kappa$]^{$\kappa$}$ }, journal = {Fundamenta Mathematicae}, volume = {177}, year = {2003}, pages = {139-149}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm177-2-3} }
David Asperó. On simple partitions of $[κ]^{κ}$ . Fundamenta Mathematicae, Tome 177 (2003) pp. 139-149. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm177-2-3/