Webthe introduction in [5, 6]). The proofs of these results often rely on forcing methods, such as in [18, 16]. For further discussions on the Halpern-L¨auchli theorem and its generalizations, refer to [5, 6, 17]. In this paper, we will prove some generalizations of the Halpern-L”auchli WebIn Part I of this series [5], we introduced a class of notions of forcing which we call Σ-Prikry, and showed that many of the known Prikry-type notions of forcing that centers around singular cardinals of countable cofinality are Σ-Prikry.We proved that given a Σ-Prikry poset ℙ and a ℙ-name for a nonreflecting stationary set T, there exists a corresponding Σ-Prikry …

COFINAL TYPES OF ULTRAFILTERS OVER MEASURABLE …

WebPrikry-typeforcingandminimalα-degree Yang Sen October 8, 2024 Abstract In this paper, we introduce several classes of Prikry-type forcing notions, two of which are used to produce minimal generic extensions, and the third is applied in α-recursion theory to produce minimal covers. The first forcing as a warm up yields a minimal generic ex- WebDec 10, 2009 · The basic problem is to determine all the possible values of 2 κ for a cardinal κ. Paul Cohen proved the independence of CH and invented the method of forcing. Easton … heihu.live

Prikry-type forcing and the set of possible cofinalities

WebPrikry forcing, de ne the -tree and uncover some of its features. The proof that the Complete Prikry Property implies the Prikry Property and the Strong Prikry Property may be found … Web1. Introduction Let κ be a singular cardinal violating GCH or a measurable with 2κ > κ+.The strength of this hypotheses was studied in [Git1,2] and [Git-Mit] combining Shelah’s pcf Webstrongly compact cardinal. This was because Prikry forcing above a strongly compact car-dinal adds a weak square sequence, which destroys the strong compactness of the smaller cardinal. Magidor overcame this difficulty by inventing yet another technique for producing non-supercompact strongly compact cardinals. Rather than iterating Prikry ... heiik