Radin forcing and its iterations

13 years 5 months ago

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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 iterating Radin forcing. First we show how to iterate Radin forcing over the same cardinal inﬁnitely many times. Secondly we show that Magidor’s method of iterating Prikry forcing over diﬀerent cardinals can be extended to iterate Radin forcing. Radin forcing was introduced in [8]. Mitchell [7] presented a version of Radin forcing which uses coherent sequences of ultraﬁlters in place of a measure sequence. Foreman and Woodin [5] developed a supercompact version of Radin forcing using measure sequences in the context of a proof that GCH can fail for every cardinal. See [2] for a more rec...

John Krueger

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