PFA(S)[S] and Locally Compact Normal Spaces

TL;DR

This paper characterizes certain locally compact normal spaces under PFA(S)[S], identifying conditions for paracompactness and countable tightness based on the absence of perfect pre-images of omega_1 and Lindelof properties of separable closed subspaces.

Contribution

It provides a characterization of paracompact, countably tight locally compact normal spaces in models of PFA(S)[S], linking topological properties to the absence of perfect pre-images of omega_1.

Findings

Paracompact, countably tight spaces exclude perfect pre-images of omega_1.

Separable closed subspaces in these spaces are Lindelof.

Characterization holds within models of PFA(S)[S].

Abstract

We examine locally compact normal spaces in models of form PFA(S)[S], in particular characterizing paracompact, countably tight ones as those which include no perfect pre-image of omega_1 and in which all separable closed subspaces are Lindelof.