If V=L, and μ, κ and λ are three infinite cardinals
with μ=cf(μ)<κ=cf(κ)≤λ, then, as
shown in \cite{Heaven}, the μ-club filters on Pκ​(λ) and
Pκ​(λ<κ) are isomorphic if and only if cf(λ)î€ =μ. Now in L, λ<κ equals u(κ,λ) (the least size of a cofinal subset in (Pκ​(λ),⊆)) equals λ if cf(λ)≥κ, and
λ+ otherwise. We show that, in ZFC, there are many triples (μ,κ,λ) for which (u(κ,λ)>λ and) the
μ-club filters on Pκ​(λ) and Pκ​(u(κ,λ))
are isomorphic