We introduce two generalized condensation principles: Local Club Condensation and Stationary Condensation. We show that while Strong Condensation (a generalized condensation principle introduced by Hugh Woodin) is inconsistent with an ω₁-Erdős cardinal, Stationary Condensation and Local Club Condensation (which should be thought of as weakenings of Strong Condensation) are both consistent with ω-superstrong cardinals.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm215-2-3,
author = {Sy-David Friedman and Peter Holy},
title = {Condensation and large cardinals},
journal = {Fundamenta Mathematicae},
volume = {215},
year = {2011},
pages = {133-166},
zbl = {1258.03074},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm215-2-3}
}
Sy-David Friedman; Peter Holy. Condensation and large cardinals. Fundamenta Mathematicae, Tome 215 (2011) pp. 133-166. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm215-2-3/