Two-cardinal versions of weak compactness: Partitions of pairs

We study various partition properties on Pκ(λ)Pκ(λ). Our main result asserts that if λ<λ<κ=λ<κλ<λ<κ=λ<κ, then (p(NShκ,λ<κ))+→(NSSκ,λ+)2, where p:Pκ(λ<κ)→Pκ(λ)p:Pκ(λ<κ)→Pκ(λ) is defined by p(x)=x∩λp(x)=x∩λ.

► The paper is concerned with partition properties on Pκ(λ)Pκ(λ) and associated ideals. ► The main result states that if λ<λ=λλ<λ=λ, then NShκ,λ+→(NSSκ,λ+)2. ► A similar result is shown to hold in case cf(λ)<κ.