Abstract
Let μ<κ<λ be three infinite cardinals, the first two being regular. We show that if there is no inner model with large cardinals, u(κ,λ) is regular, where u(κ,λ) denotes the least size of a cofinal subset in (Pκ(λ),⊆), and cf(λ)≠μ, then (a) the μ-club filters on Pκ(λ) and Pκ(u(κ,λ)) are isomorphic, and (b) the ideal dual to the μ-club filter on Pκ(λ) (and hence the restriction of the nonstationary ideal on Pκ(λ) to sets of uniform cofinality μ) is not Iκ,λ-bu(κ,λ)-saturated.
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