This e-book 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 unfastened subalgebras, and cellularity, which supplies the supremum of cardinalities of units of pairwise disjoint parts. Twenty-one such features are studied intimately, and plenty of extra in passing. The questions thought of are the behaviour of those capabilities lower than algebraic operations resembling items, unfastened items, ultraproducts, and their relationships to at least one another.
Assuming familiarity with in basic terms the fundamentals of Boolean algebras and set thought, via easy countless combinatorics and forcing, the e-book studies present wisdom approximately those services, giving whole proofs for many evidence. a distinct function of the e-book 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 a similar writer, the current paintings is way better than both of those. It includes ideas to a number of the 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 e-book summarize the relationships among the services for lots of very important periods of Boolean algebras, together with period algebras, tree algebras and superatomic algebras.
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