Absoluteness via resurrection

Generic absoluteness

We explore the consistency strength of 1 3 and 1 4 absoluteness, for a variety of forcing notions.

Forcing absoluteness and regularity properties

Σ3-Absoluteness in Forcing Extensions

We investigate the consistency strength of the forcing axiom for Σ3 formulas, for various classes of forcings. We review that the consistency strength of Σ3-absoluteness for all set forcing or even just for ω1-preserving forcing is that of a reflecting cardinal. To get the same strength from the forcing axiom restricted to proper forcing, one can add the hypotheses that ω1 is inaccessible to re...

Resurrection

The golden era of molecular biology has paved the way for us now to tweak, fix, engineer, or even entirely synthesize genomes at levels and scales never seen before. Sequencing technologies continue to improve at exponential rates and have yielded powerful new insights into organisms of the distant past, as well as those that co-inhabit the planet with us. The era of genomics has ushered in the...

Axioms of Generic Absoluteness

We give a unified presentation of the set-theoretic axioms of generic absoluteness, we survey the known results regarding their consistency strength and some of their consequences as well as their relationship to other kinds of set-theoretic axioms, and we provide a list of the main open problems.