Preservation of Topological Properties by Strongly Proper Forcings
arXiv:2408.02495
Abstract
In this paper we show that forcings which are strongly proper for stationarily many countable elementary submodels preserve each of the following properties of topological spaces: countably tight; Lindelöf; Rothberger; Menger; and a strategic version of Rothberger. This extends results from Dow, as well as from Iwasa and from Kada.