Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
A hull of A ⊆ [0,1] is a set H containing A such that λ*(H) = λ*(A). We investigate all four versions of the following problem. Does there exist a monotone (with respect to inclusion) map that assigns a Borel/$G_{δ}$ hull to every negligible/measurable subset of [0,1]?
Three versions turn out to be independent of ZFC, while in the fourth case we only prove that the nonexistence of a monotone $G_{δ}$ hull operation for all measurable sets is consistent. It remains open whether existence here is also consistent. We also answer the question of Z. Gyenes and D. Pálvölgyi whether monotone hulls can be defined for every chain of measurable sets. Moreover, we comment on the problem of hulls of all subsets of [0,1].
Three versions turn out to be independent of ZFC, while in the fourth case we only prove that the nonexistence of a monotone $G_{δ}$ hull operation for all measurable sets is consistent. It remains open whether existence here is also consistent. We also answer the question of Z. Gyenes and D. Pálvölgyi whether monotone hulls can be defined for every chain of measurable sets. Moreover, we comment on the problem of hulls of all subsets of [0,1].
Słowa kluczowe
Kategorie tematyczne
- 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
- 03E17: Cardinal characteristics of the continuum
- 28A51: Lifting theory
- 28E15: Other connections with logic and set theory
- 03E15: Descriptive set theory
- 03E35: Consistency and independence results
- 28A05: Classes of sets (Borel fields, σ -rings, etc.), measurable sets, Suslin sets, analytic sets
Czasopismo
Rocznik
Tom
Numer
Strony
105-115
Opis fizyczny
Daty
wydano
2009
Twórcy
autor
- Rényi Alfréd Institute of Mathematics, Hungarian Academy of Sciences, P.O. Box 127, H-1364 Budapest, Hungary
autor
- Eötvös Loránd University, Department of Analysis, Pázmány Péter sétány 1/c, H-1117 Budapest, Hungary
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-fm205-2-2