Is 𝓟(ω) a subalgebra?

Alan Dow, and Ilijas Farah. "Is 𝓟(ω) a subalgebra?." Fundamenta Mathematicae 183.2 (2004): 91-108. <http://eudml.org/doc/282934>.

@article{AlanDow2004,
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.},
author = {Alan Dow, Ilijas Farah},
journal = {Fundamenta Mathematicae},
keywords = {; Open Coloring Axiom},
language = {eng},
number = {2},
pages = {91-108},
title = {Is 𝓟(ω) a subalgebra?},
url = {http://eudml.org/doc/282934},
volume = {183},
year = {2004},
}

TY - JOUR
AU - Alan Dow
AU - Ilijas Farah
TI - Is 𝓟(ω) a subalgebra?
JO - Fundamenta Mathematicae
PY - 2004
VL - 183
IS - 2
SP - 91
EP - 108
AB - 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.
LA - eng
KW - ; Open Coloring Axiom
UR - http://eudml.org/doc/282934
ER -