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Prikry on extenders, revisited

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The extender based forcing of Gitik and Magidor is generalized to yield, given any extender j: V å M with critical point κ, a cardinal preserving generic extension with no new bounded subset of κ in which cf(κ) = ω and \(\kappa ^\omega = |j(\kappa )|\).

Assuming a superstrong cardinal exists, the forcing notion is used to construct a model in which the added Prikry sequences are a scale in the normal Prikry sequence.

In addition, several ways to produce generic filter over an iterated ultrapower are presented.

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The writing of this paper was partially supported by the Israel Science Foundation

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Merimovich, C. Prikry on extenders, revisited. Isr. J. Math. 160, 253–280 (2007).

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