Is 𝓟(ω) a subalgebra?

• Autorzy: Alan Dow , Ilijas Farah
• Języki publikacji: EN

Abstrakty

EN

We consider the question of whether 𝒫(ω) is a subalgebra whenever it is a quotient of a Boolean algebra by a countably generated ideal. This question was raised privately by Murray Bell. We obtain two partial answers under the open coloring axiom. Topologically our first result is that if a zero-dimensional compact space has a zero-set mapping onto βℕ, then it has a regular closed zero-set mapping onto βℕ. The second result is that if the compact space has density at most ω₁, then it will map onto βℕ if it contains a zero-set that maps onto βℕ.

Kategorie tematyczne

• 54A35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2004
• Tom: 183
• Numer: 2
• Strony: 91-108

Daty

wydano

2004

Twórcy

autor

Alan Dow

• Department of Mathematics, UNC-Charlotte, 9201 University City Blvd., Charlotte, NC 28223-0001, U.S.A.

autor

Ilijas Farah

• Department of Mathematics and Statistics, York University, 4700 Keele Street, North York, Ontario, Canada, M3J 1P3
• Matematicki Institut, Kneza Mihaila 35, Beograd, Serbia and Montenegro

Identyfikatory

DOI

10.4064/fm183-2-1