A simultaneous generalization of independence and disjointness in boolean algebras

Details A simultaneous generalization of independence and disjointness in boolean algebras A simultaneous generalization of independence and disjointness in boolean algebras

2009-11-26

arxiv.org/abs/0911.5124v3

Mathematics

Logic

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Scientific paper

10.1007/s11083-011-9237-x

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 omega-free boolean algebras) are investigated. These include connections to hypergraph theory and cardinal invariants on these algebras. Related cardinal functions, $n$Ind, which is the supremum of the cardinalities of n-independent subsets; i_n, the minimum size of a maximal n-independent subset; and i_omega, the minimum size of an omega-independent subset, are introduced and investigated. The values of i_n and i_omega on P(omega)/fin are shown to be independent of ZFC.

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