Partition properties of subsets of $\mathcal P_\kappa \lambda$
Volume 161 / 1999
Fundamenta Mathematicae 161 (1999), 325-329
DOI: 10.4064/fm-161-3-325-329
Abstract
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 $f : ∪_{n < ω}[X]^{n}_⊂ → γ$ with $X⊂P_κλ$ unbounded and 1 < γ < κ there is an unbounded Y ∪ X with $|f''[Y]^n_⊂| = 1$ for any n < ω.
