By J. Donald Monk
This ebook is anxious with cardinal quantity valued services outlined for any Boolean algebra. Examples of such services are independence, which assigns to every Boolean algebra the supremum of the cardinalities of its unfastened subalgebras, and cellularity, which provides the supremum of cardinalities of units of pairwise disjoint components. Twenty-one such features are studied intimately, and plenty of extra in passing. The questions thought of are the behaviour of those features less than algebraic operations similar to items, unfastened items, ultraproducts, and their relationships to 1 another.
Assuming familiarity with purely the fundamentals of Boolean algebras and set conception, via uncomplicated countless combinatorics and forcing, the publication experiences present wisdom approximately those services, giving entire proofs for many evidence. a unique function of the ebook is the eye given to open difficulties, of which 185 are formulated.
Based on Cardinal features on Boolean Algebras (1990) and Cardinal Invariants on Boolean Algebras (1996) via an identical writer, the current paintings is way higher than both of those. It comprises strategies to the various open difficulties of the sooner volumes. one of the new issues are continuum cardinals on Boolean algebras, with a long therapy of the reaping quantity. Diagrams on the finish of the booklet summarize the relationships among the features for lots of vital periods of Boolean algebras, together with period algebras, tree algebras and superatomic algebras.
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