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Displaying similar documents to “Stationary reflection in extender models”

Condensation and large cardinals

Sy-David Friedman, Peter Holy (2011)

Fundamenta Mathematicae

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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.