Q-Sets, \Delta-Sets, and L-Spaces
Pourya Memarpanahi, Paul Szeptycki

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 -set space is considered. We show that J. Moore's ZFC -space is not a Q-set space in ZFC and, assuming all Aronszajn trees are special, it is not a -set space.
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Taxonomy
TopicsFuzzy and Soft Set Theory
