Compact covering mappings and cofinal families of compact subsets of a Borel set
Volume 167 / 2001
Fundamenta Mathematicae 167 (2001), 213-249
MSC: Primary 03E15; Secondary 03E45, 54H05.
DOI: 10.4064/fm167-3-2
Abstract
Among other results we prove that the topological statement “Any compact covering mapping between two ${\bf \Pi }^0_{3}$ spaces is inductively perfect” is equivalent to the set-theoretical statement “$\forall \alpha \in \omega ^\omega ,$ $\omega _1^{L(\alpha )}<\omega _1$”; and that the statement “Any compact covering mapping between two coanalytic spaces is inductively perfect” is equivalent to “Analytic Determinacy”. We also prove that these statements are connected to some regularity properties of coanalytic cofinal sets in ${\cal K}(X)$, the hyperspace of all compact subsets of a Borel set $X$.
