Variations of Independence in Boolean Algebras

Simple item page
dc.creatorBruns, Corey Thomas
dc.date2008-11-17
dc.date2008-11-18
dc.date.accessioned2026-07-07T10:18:46Z
dc.date.available2026-07-07T10:18:46Z
dc.descriptionWe 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. Ideal-independence is also considered, and it is shown that the cardinal function p <= s_mm for infinite boolean algebras. We also define and consider moderately generated boolean algebras; that is, those boolean algebras that have a generating set consisting of elements that split finitely many elements of the boolean algebra.
dc.descriptionPhD thesis
dc.identifierhttps://arxiv.org/abs/0811.2610
dc.identifierhttp://arxiv.org/abs/0811.2610
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/174303
dc.subjectLogic
dc.subject03G05; 03E17
dc.titleVariations of Independence in Boolean Algebras
dc.typetext

Files

Collections

arXiv