Geodesic
Partition properties of subsets of $\mathcal P_\kappa \lambda$
Fundamenta Mathematicae, Tome 161 (1999) no. 3, pp. 325-329
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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. 
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     title = {Partition properties of subsets of $\mathcal P_\kappa \lambda$},
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Masahiro Shioya. Partition properties of subsets of $\mathcal P_\kappa \lambda$. Fundamenta Mathematicae, Tome 161 (1999) no. 3, pp. 325-329. doi: 10.4064/fm-161-3-325-329

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