Giorgio Audrito, Matteo Viale
Published 2014-04-08, updated 2015-06-03Version 3
The resurrection axioms are forms of forcing axioms that were introduced recently by Hamkins and Johnstone, developing on ideas of Chalons and Velickovic. We introduce a stronger form of resurrection axioms (the iterated resurrection axioms) and show that they imply generic absoluteness for the first-order theory of $H_{\mathfrak{c}}$ with parameters with respect to various classes of forcing. We also show that the consistency strength of these axioms is below that of a Mahlo cardinal for most forcing classes, and below that of a stationary limit of supercompact cardinals for the class of stationary set preserving posets. We also compare these results with the generic absoluteness results by Woodin and the second author.
Forcing "$\mathrm{NS}_{ω_1}$ is $ω_1$-dense" From Large Cardinals
Menas' result is best possible
On Indestructible Strongly Guessing Models
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