1Equipe d'Analyse Université Paris 6 Boîte 186 4, place Jussieu 75252 Paris CEDEX 05, France 2Equipe d'Analyse Université Paris 6 Boite 186 4, place Jussieu 75252 Paris CEDEX 05, France
Fundamenta Mathematicae, Tome 167 (2001) no. 3, pp. 213-249
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
$X$.
Keywords:
among other results prove topological statement compact covering mapping between spaces inductively perfect equivalent set theoretical statement forall alpha omega omega omega alpha omega statement compact covering mapping between coanalytic spaces inductively perfect equivalent analytic determinacy prove these statements connected regularity properties coanalytic cofinal sets cal hyperspace compact subsets borel set
Affiliations des auteurs :
G. Debs
1
;
J. Saint Raymond
2
1
Equipe d'Analyse Université Paris 6 Boîte 186 4, place Jussieu 75252 Paris CEDEX 05, France
2
Equipe d'Analyse Université Paris 6 Boite 186 4, place Jussieu 75252 Paris CEDEX 05, France
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author = {G. Debs and J. Saint Raymond},
title = {Compact covering mappings and
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journal = {Fundamenta Mathematicae},
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AU - J. Saint Raymond
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cofinal families of compact subsets of a Borel set
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cofinal families of compact subsets of a Borel set
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G. Debs; J. Saint Raymond. Compact covering mappings and
cofinal families of compact subsets of a Borel set. Fundamenta Mathematicae, Tome 167 (2001) no. 3, pp. 213-249. doi: 10.4064/fm167-3-2
