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Cardinal Invariants on Boolean Algebras
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153 b
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This book is concerned with cardinal number valued functions defined for any Boolean algebra. Examples of such functions are independence, which assigns to each Boolean algebra the supremum of the cardinalities of its free subalgebras, and cellularity, which gives the supremum of cardinalities of sets of pairwise disjoint elements.§The questions considered are the behaviour of these functions under algebraic operations such as products, free products, ultraproducts, and their relationship to one another. Assuming familiarity with only the basics of Boolean algebras and set theory, the book reviews current knowledge about these functions, giving complete proofs for most facts. A special feature of the book is the attention given to open problems, of which 97 are formulated.§Diagrams at the end of the book summarize the relationships between the functions for many important classes of Boolean algebras, including tree algebra and superatomic algebras.
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