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, Volume 30, Issue 1, pp 211–231 | Cite as

A Simultaneous Generalization of Independence and Disjointness in Boolean Algebras

  • Corey Thomas Bruns
Article

Abstract

We give a definition of some classes of boolean algebras generalizing free boolean algebras; they satisfy a universal property that certain functions extend to homomorphisms. We give a combinatorial property of generating sets of these algebras, which we call n-independent. The properties of these classes (n-free and ω-free boolean algebras) are investigated. These include connections to hypergraph theory and cardinal invariants on these algebras. Related cardinal functions, \(\mathfrak{i}_{n}\), the minimum size of a maximal n-independent subset and \(\mathfrak{i}_{\omega}\), the minimum size of an ω-independent subset, are introduced and investigated. The values of \(\mathfrak {i}_{n}\) and \(\mathfrak {i}_{\omega}\) on Open image in new window are shown to be independent of ZFC.

Keywords

Boolean algebra Independence Delta system Forcing 

Mathematics Subject Classifications (2010)

Primary: 03G05; Secondary: 03E17 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Mathematical and Computer SciencesUniversity of Wisconsin-WhitewaterWhitewaterUSA

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