Compact covering mappings and cofinal families of compact subsets of a Borel set

• Autorzy: G. Debs , J. Saint Raymond
• Języki publikacji: EN

Abstrakty

EN

Among other results we prove that the topological statement "Any compact covering mapping between two Π⁰₃ spaces is inductively perfect" is equivalent to the set-theoretical statement "$∀α ∈ ω^{ω}, ω₁^{L(α)} < ω₁$"; 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 𝒦(X), the hyperspace of all compact subsets of a Borel set X.

Kategorie tematyczne

• 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
• 03E15: Descriptive set theory
• 03E45: Inner models, including constructibility, ordinal definability, and core models

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2001
• Tom: 167
• Numer: 3
• Strony: 213-249

Daty

wydano

2001

Twórcy

autor

G. Debs

• Equipe d'Analyse, Université Paris 6, Boîte 186, 4, place Jussieu, 75252 Paris CEDEX 05, France

autor

J. Saint Raymond

• Equipe d'Analyse, Université Paris 6, Boite 186, 4, place Jussieu, 75252 Paris CEDEX 05, France

Identyfikatory

DOI

10.4064/fm167-3-2