David Asperó, Asaf Karagila
Published 2018-06-11Version 1
We observe that Dependent Choice is a sufficient choice principle for developing the basic theory of proper forcing, and for deriving generic absoluteness for the Chang model in the presence of large cardinals. We also investigate some basic consequences of the Proper Forcing Axiom in ZF, and formulate a natural question about the generic absoluteness of the Proper Forcing Axiom in ZF+DC and ZFC.
Properness under closed forcing
The proper forcing axiom for $\aleph_1$-sized posets and the size of the continuum
Does $\mathsf{DC}$ imply $\mathsf{AC}_ω$, uniformly?
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