Cofinal $Σ^1_1$ and $Π^1_1$ subsets of $ω^ω$
Volume 159 / 1999
Fundamenta Mathematicae 159 (1999), 161-193
DOI: 10.4064/fm-159-2-161-193
Abstract
We study properties of $∑^1_1$ and $π^1_1$ subsets of $ω^ω$ that are cofinal relative to the orders ≤ (≤*) of full (eventual) domination. We apply these results to prove that the topological statement "Any compact covering mapping from a Borel space onto a Polish space is inductively perfect" is equivalent to the statement "$∀α ∈ω^ω, ω^ω ∩ L(α )$ is bounded for ≤*".
