Prikry forcing and tree Prikry forcing of various filters
نویسندگان
چکیده
منابع مشابه
Mathias-Prikry and Laver-Prikry type forcing
We study the Mathias-Prikry and Laver-Prikry forcings associated with filters on ω. We give a combinatorial characterization of Martin’s number for these forcing notions and present a general scheme for analyzing preservation properties for them. In particular, we give a combinatorial characterization of those filters for which the Mathias-Prikry forcing does not add any dominating reals.
متن کاملHybrid Prikry Forcing
We present a new forcing notion combining diagonal supercompact Prikry focing with interleaved extender based forcing. We start with a supercompact cardinal κ. In the final model the cofinality of κ is ω, the singular cardinal hypothesis fails at κ and GCH holds below κ. Moreover we define a scale at κ, which has a stationary set of bad points in the ground model.
متن کاملSupercompact extender based Prikry forcing
The extender based Prikry forcing notion is being generalized to supercompact extenders.
متن کاملPrikry Forcing with Long Extenders
In this note, we go through Gitik’s Long Extender forcing. In order to motivate it, work through the basic Pirkry forcing as well as the diagonal Prikry forcing. The presentation here is based on Spencer Unger’s lectures from the 2015 GSST in addition to Gitik’s Handbook chapter.
متن کاملGeneralized Prikry forcing and iteration of generic ultrapowers
Moreover Bukovský [1] and Dehornoy [2] showed that the generic extension Mω[〈j0,n(κ) | n ∈ ω〉] is ⋂ n∈ω Mn in Theorem 1.1. (For the history of these results, read the introduction of Dehornoy [2] and pp.259-260 of Kanamori [6]. ) In Dehornoy [3], these results were generalized for the forcing of Magidor [7] which changes a measurable cardinal of higher Mitchell order into a singular cardinal of...
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ژورنال
عنوان ژورنال: Archive for Mathematical Logic
سال: 2019
ISSN: 0933-5846,1432-0665
DOI: 10.1007/s00153-019-00660-3