Dropping cofinalities
نویسنده
چکیده
Our aim is to present constructions in which some of the cofinalities drop down, i.e. the generators of PCF structure are far a part. 1 Some Preliminary Settings Let λ0 < κ0 < λ1 < κ1 < ... < λn < κn < ...., n < ω be a sequence of cardinals such that for each n < ω • λn is λ +n+2 n +2 n strong as witnessed by an extender Eλn • κn is κ +n+2 n +2 n strong as witnessed by an extender Eκn Let κ = ⋃ n<ω κn. Fix some regular θ > θ ′ ≥ κ. Our aim will be to make 2 = θ, but so that each cofinality from the interval [κ, θ′] is obtained using only indiscernibles related to λn’s. Let us force first with the preparation forcing P ′ of [6]. The assignment function of [6] is used here for models of cardinalities below θ′ intersected with H(θ′) but with range over λn’s. We will use names of indiscernibles for λn’s to define the assignment to κn’s. Models of cardinalities in [κ, θ′] will be assigned to those of cardinalities of this indiscernibles, so a way below κn’s. We deal first with the simplest case: θ = κ and θ′ = κ. Such situation was considered in [3], but our approach here is different and generalizes to arbitrary θ, θ′.
منابع مشابه
Dropping cofinalities and gaps
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تاریخ انتشار 2006