We investigate the problem of when ≤λ-support iterations of < λ-complete notions of forcing preserve λ⁺. 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 Rosłanowski 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 [4].
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm179-3-4,
author = {Todd Eisworth},
title = {On iterated forcing for successors of regular cardinals},
journal = {Fundamenta Mathematicae},
volume = {177},
year = {2003},
pages = {249-266},
zbl = {1066.03051},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm179-3-4}
}
Todd Eisworth. On iterated forcing for successors of regular cardinals. Fundamenta Mathematicae, Tome 177 (2003) pp. 249-266. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm179-3-4/