Abstract:
In this joint work with Philipp Schlicht we show that it is possible to change the cardinality of an infinite set of Cohen reals without collapsing cardinals. We consider some other notions of "collapsing" forcings which do not collapse cardinals, and time permitting we will discuss some characterisations of Dedekind-finite sets which remain Dedekind-finite after adding a Cohen subset.
This appears in https://arxiv.org/abs/1910.14480