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 | Abstract: | 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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