Faculty Publications

On Iterated Forcing For Successors Of Regular Cardinals

Document Type

Article

Keywords

Proper forcing, Uncountable support iterations

Journal/Book/Conference Title

Fundamenta Mathematicae

Volume

179

Issue

3

First Page

249

Last Page

266

Abstract

We investigate the problem of when ≤λ-support iterations of <-complete notions of forcing preserveλ+. We isolate a property - properness over diamonds - that implies λ+ is preserved and show that this property is preserved by λ-support iterations. Our condition is a relative of that presented by Roslanowski and Shelah in [2]; it is not clear if the two conditions are equivalent. We close with an application of our technology by presenting a consistency result on uniformizing colorings of ladder systems on {δ < λ+ : cf(δ) = λ} that complements a theorem of Shelah.

Original Publication Date

1-1-2003

DOI of published version

10.4064/fm179-3-4

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