منابع مشابه
Extender Based Radin Forcing
We define extender sequences, generalizing measure sequences of Radin forcing. Using the extender sequences, we show how to combine the Gitik-Magidor forcing for adding many Prikry sequenes with Radin forcing. We show that this forcing satisfies a Prikry like condition destroys no cardinals, and has a kind of properness. Depending on the large cardinals we start with this forcing can blow the p...
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We analyze the modified extender based forcing from Assaf Sharon’s PhD thesis. We show there is a bad scale in the extension and therefore weak square fails. We also present two metatheorems which give a rough characterization of when a diagonal Prikry-type forcing forces the failure of weak square.
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In this paper we consider two methods for producing models with some global behavior of the continuum function on singular cardinals and the failure of weak square. The first method is as an extension of Sinapova’s work [21]. We define a diagonal supercompact Radin forcing which adds a club subset to a cardinal κ while forcing the failure of SCH everywhere on the club. The intuition from Sinapo...
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The extender based Prikry forcing notion is being generalized to supercompact extenders.
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We provide an exposition of supercompact Radin forcing and present several methods for iterating Radin forcing. In this paper we give an exposition of supercompact Radin forcing using coherent sequences of ultrafilters. This version of Radin forcing includes as special cases the Prikry forcing and Magidor forcing, both the measurable and supercompact versions. We also introduce some methods for...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2003
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-03-03202-1