Condensation and large cardinals
Volume 215 / 2011
Fundamenta Mathematicae 215 (2011), 133-166 MSC: 03E35, 03E55. DOI: 10.4064/fm215-2-3
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 $\omega _1$-Erdős cardinal, Stationary Condensation and Local Club Condensation (which should be thought of as weakenings of Strong Condensation) are both consistent with $\omega $-superstrong cardinals.