Authors: Dow, Alan
Farah, Ilijas 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Is P(ω) a subalgebra?
Journal: Fundamenta Mathematicae
Volume: 183
Issue: 2
First page: 91
Last page: 108
Issue Date: 1-Jan-2004
Rank: M22
ISSN: 0016-2736
DOI: 10.4064/fm183-2-1
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.
Keywords: Open Coloring Axiom | βN
Publisher: Instytut Matematyczny Polskiej Akademii Nauk

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