An ℵ1-dense ideal on ℵ2

This paper establishes the consistency of a countably complete, uniform, ℵ₁-dense ideal on ℵ₂. As a corollary, it is consistent that there exists a uniform ultrafilterD on ω₂ such that |ω ₁ ^ω2 D|=ω₁. A general “transfer” result establishes the consistency of countably complete uniform ideal K on ω₂ such thatP(ω₂)/K≅P(ω₁)/ {countable sets}. Partially supported by an NSF grant.