This ebook is worried with cardinal quantity valued capabilities 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 supplies the supremum of cardinalities of units of pairwise disjoint parts. Twenty-one such services are studied intimately, and plenty of extra in passing. The questions thought of are the behaviour of those capabilities below algebraic operations reminiscent of items, loose items, ultraproducts, and their relationships to at least one another.
Assuming familiarity with simply the fundamentals of Boolean algebras and set idea, via basic limitless combinatorics and forcing, the ebook experiences present wisdom approximately those capabilities, giving entire proofs for many proof. a distinct function of the booklet is the eye given to open difficulties, of which 185 are formulated.
Based on Cardinal capabilities on Boolean Algebras (1990) and Cardinal Invariants on Boolean Algebras (1996) through an identical writer, the current paintings is way better than both of those. It comprises recommendations to some of the open difficulties of the sooner volumes. one of the new themes are continuum cardinals on Boolean algebras, with a long therapy of the reaping quantity. Diagrams on the finish of the ebook summarize the relationships among the capabilities for plenty of vital periods of Boolean algebras, together with period algebras, tree algebras and superatomic algebras.
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