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
Recommended Citation
Eisworth, Todd, "On Iterated Forcing For Successors Of Regular Cardinals" (2003). Faculty Publications. 3304.
https://scholarworks.uni.edu/facpub/3304
