Combining Short extenders forcings with Extender based Prikry
نویسنده
چکیده
Change first the cofinality of κ to ω by adding a Prikry sequence ⟨κn | n < ω⟩ such that each κn is κ +n+2 n –strong. Then use the short extenders forcing which adds κ +ω+2 many cofinal ω-sequences to κ (after the preparation or simultaneously with it). All cardinals will be preserved then. If one does not care about falling of κ, then preform Gap 2 short extenders forcing. As a result κ will turn into κ of the extension.
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