Q-Sets, \Delta-Sets, and L-Spaces

TL;DR

This paper investigates the existence of Lindelöf Q-set and Δ-set spaces, demonstrating that certain known L-spaces are not Q-sets or Δ-sets under specific set-theoretic assumptions.

Contribution

It proves that J. Moore's ZFC L-space is not a Q-set space in ZFC and not a Δ-set space assuming all Aronszajn trees are special.

Findings

J. Moore's ZFC L-space is not a Q-set space in ZFC

Under the assumption that all Aronszajn trees are special, the L-space is not a Δ-set space

The results depend on set-theoretic assumptions about Aronszajn trees

Abstract

The question whether there is a Lindelof Q-set space or Lindelof $\Delta$-set space is considered. We show that J. Moore's ZFC $L$-space is not a Q-set space in ZFC and, assuming all Aronszajn trees are special, it is not a $\Delta$-set space.