We generalize the notion of a fat subset of a regular cardinal κ to a fat subset of , where κ ⊆ X. Suppose μ < κ, , and κ is supercompact. Then there is a generic extension in which κ = μ⁺⁺, and for all regular λ ≥ μ⁺⁺, there are stationarily many N in which are internally club but not internally approachable.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm201-2-2,
author = {John Krueger},
title = {Internally club and approachable for larger structures},
journal = {Fundamenta Mathematicae},
volume = {201},
year = {2008},
pages = {115-129},
zbl = {1167.03029},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm201-2-2}
}
John Krueger. Internally club and approachable for larger structures. Fundamenta Mathematicae, Tome 201 (2008) pp. 115-129. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm201-2-2/