Abstract
First of all, note that if F is a non-principal ultrafilter on a BA A, then πχF ≥ ω. To see this, suppose that X is a finite set of non-zero elements of A which is dense in F Choose y ∈ F such that y < Π(X ⋂ F). Then choose x ∈ X such that x ≤ y · Π{z ∈ F : -z ∈ X}. This clearly gives a contradiction, whether x ∈ F or not.
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© 1990 Springer Basel AG
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Monk, J.D. (1990). π-Character. In: Cardinal Functions on Boolean Algebras. Lectures in Mathematics. ETH Zürich. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6381-0_10
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DOI: https://doi.org/10.1007/978-3-0348-6381-0_10
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-2495-7
Online ISBN: 978-3-0348-6381-0
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