Independent families in Boolean algebras with some separation properties

Piotr Koszmider; Saharon Shelah

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arXiv · 1209.0177

Independent families in Boolean algebras with some separation properties

Piotr Koszmider·Saharon Shelah

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Abstract

We prove that any Boolean algebra with the subsequential completeness property contains an independent family of size continuum. This improves a result of Argyros from the 80ties which asserted the existence of an uncountable independent family. In fact we prove it for a bigger class of Boolean algebras satisfying much weaker properties. It follows that the Stone spaces of all such Boolean algebras contains a copy of the Cech-Stone compactification of the integers and the Banach space of contnuous functions on them has $l_\infty$ as a quotient. Connections with the Grothendieck property in Banach spaces are discussed.

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BibTeX RIS

Piotr Koszmider, Saharon Shelah. 2012-09-02. Independent families in Boolean algebras with some separation properties. https://arxiv.org/abs/1209.0177

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