Preservation of Topological Properties by Strongly Proper Forcings

TL;DR

This paper demonstrates that strongly proper forcings for stationarily many models preserve key topological properties such as Lindelöfness and Rothberger, extending previous results in the field.

Contribution

It establishes that strongly proper forcings for stationarily many models preserve several important topological properties, broadening the understanding of their impact.

Findings

Strongly proper forcings preserve Lindelöf spaces.

They also preserve Rothberger and Menger properties.

Results extend previous work by Dow, Iwasa, and Kada.

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; Lindel\"of; Rothberger; Menger; and a strategic version of Rothberger. This extends results from Dow, as well as from Iwasa and from Kada.