By J. Donald Monk
This publication is anxious with cardinal quantity valued capabilities outlined for any Boolean algebra. Examples of such features 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 lots of extra in passing. The questions thought of are the behaviour of those capabilities less than algebraic operations comparable to items, unfastened items, ultraproducts, and their relationships to at least one another.
Assuming familiarity with merely the fundamentals of Boolean algebras and set conception, via easy limitless combinatorics and forcing, the ebook reports present wisdom approximately those features, giving entire proofs for many evidence. a distinct function of the ebook 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) by means of an analogous writer, the current paintings is far greater than both of those. It comprises options to some of the open difficulties of the sooner volumes. one of the new issues are continuum cardinals on Boolean algebras, with a long remedy of the reaping quantity. Diagrams on the finish of the publication summarize the relationships among the services for plenty of vital periods of Boolean algebras, together with period algebras, tree algebras and superatomic algebras.
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