We study the partition relation X →w [Y]p2 that is a weakening of the usual partition relation X → [Y]ρ2. Our main result asserts that if κ is an uncountable strongly compact cardinal and 𝔡κ≤λ < κ, then Iκ,λ+ →w [Iκ,λ+]λ< κ2 does not hold.
"Weak square bracket relations for Pκ (λ)." J. Symbolic Logic 73 (3) 729 - 751, September 2008. https://doi.org/10.2178/jsl/1230396744