Dropping cofinalities and gaps

نویسنده

Moti Gitik

چکیده

Our aim is to show the consistency of 2κ ≥ κ+θ, for any θ < κ starting with a singular cardinal κ of cofinality ω so that ∀n < ω∃α < κ(o(α) = α). Dropping cofinalities technics are used for this purpose. 1 א1-gap and infinite drops in cofinalities Let κ be a singular cardinal of cofinality ω such that for each γ < κ and n < ω there is α, γ < α < κ, such that o(α) = α. We fix a sequence of cardinals κ0 < κ1 < ... < κn < ..., n < ω so that • n<ω κn = κ • for every n < ω, κn is κ n strong as witnessed by an extender Eκn • for every n < ω, the normal measure of Eκn concentrates on τ ’s which are τ + ω1 strong as witnessed by a coherent sequence of extenders 〈Eτ (ξ)|ξ < ω1〉 Fix also an increasing sequence 〈λn|n < ω〉 such that • λ0 < κ0

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