Let κ > ω be a regular cardinal and λ > κ a cardinal. The following partition property is shown to be consistent relative to a supercompact cardinal: For any with unbounded and 1 < γ < κ there is an unbounded Y ∪ X with for any n < ω.
@article{bwmeta1.element.bwnjournal-article-fmv161i3p325bwm, author = {Masahiro Shioya}, title = {Partition properties of subsets of P$\kappa$$\lambda$}, journal = {Fundamenta Mathematicae}, volume = {159}, year = {1999}, pages = {325-329}, zbl = {0937.03056}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv161i3p325bwm} }
Shioya, Masahiro. Partition properties of subsets of Pκλ. Fundamenta Mathematicae, Tome 159 (1999) pp. 325-329. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv161i3p325bwm/
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