Piotr Koszmider: Independent families in Boolean algebras with some separation properties

15/November/2013, 14:00–15:00
Fields institute, Room 210

Speaker:  Piotr Koszmider

Title:  Independent families in Boolean algebras with some separation properties

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 continuous functions on them has l-infinity as a quotient. Connections with the Grothendieck property in Banach spaces are discussed. The talk is based on the paper: Piotr Koszmider, Saharon Shelah; Independent families in Boolean algebras with some separation properties; Algebra Universalis 69 (2013), no. 4, 305 – 312

 

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