PFA(S)[S] and countably compact spaces

TL;DR

This paper explores the implications of PFA(S)[S] on countably compact spaces, demonstrating certain undecidable assertions and establishing the consistency of paracompactness in locally compact, perfectly normal spaces without large cardinals.

Contribution

It shows that under PFA(S)[S], some undecidable assertions about countably compact spaces hold, and proves the consistency of paracompactness in certain spaces without large cardinals.

Findings

Undecidable assertions about countably compact spaces hold under PFA(S)[S]

Consistency of paracompactness in locally compact, perfectly normal spaces without large cardinals

Demonstrates the influence of PFA(S)[S] on topological space properties

Abstract

We show a number of undecidable assertions concerning countably compact spaces hold under PFA(S)[S]. We also show the consistency without large cardinals of "every locally compact, perfectly normal space is paracompact".