This ebook is worried 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 loose subalgebras, and cellularity, which supplies the supremum of cardinalities of units of pairwise disjoint parts. Twenty-one such services are studied intimately, and lots of extra in passing. The questions thought of are the behaviour of those features less than algebraic operations resembling items, loose items, ultraproducts, and their relationships to at least one another.
Assuming familiarity with basically the fundamentals of Boolean algebras and set idea, via uncomplicated limitless combinatorics and forcing, the ebook studies present wisdom approximately those services, giving entire proofs for many evidence. a different function of the publication is the eye given to open difficulties, of which 185 are formulated.
Based on Cardinal services on Boolean Algebras (1990) and Cardinal Invariants on Boolean Algebras (1996) through an analogous writer, the current paintings is far greater than both of those. It includes 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 very important sessions of Boolean algebras, together with period algebras, tree algebras and superatomic algebras.
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