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Along with a simplified explanation of Boolean logic and how it is used for online searching, this guide offers reproducible worksheets that lead students through powerful strategic techniques for decision-making and researching. ... Read more

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Offering students and researchers in the behavioural and social sciences a brief and accessible introduction to the comparative method, it is ideal for students of public administration, policy, sociology, political science, social psychology, and international relations.It provides readers with basic guidelines for comparative research by addressing all key methodological issues. ... Read more

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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. Twenty-one such functions are studied in detail, and many more in passing. The questions considered are the behaviour of these functions under algebraic operations such as products, free products, ultraproducts, and their relationships to one another. Assuming familiarity with only the basics of Boolean algebras and set theory, through to simple infinite combinatorics and forcing, 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.

Based on Cardinal Functions on Boolean Algebras (1990) by the same author, the present work is nearly twice the size of the original work. It contains solutions to many of the open problems which are discussed in greater detail than before. Among the new topics considered are ultraproducts and Fedorchukís theorem, and there is a more complete treatment of the cellularity of free products. Diagrams at the end of the book summarize the relationships between the functions for many important classes of Boolean algebras, including tree algebras and superatomic algebras.

Review:

"This book is an indispensable tool for anyone working in Boolean algebra, and is also recommended for set-theoretic topologists." - Zentralblatt MATH

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The book is a fairly complete and up-to-date survey of projectivity and its generalizations in the class of Boolean algebras. Although algebra adds its own methods and questions, many of the results presented were first proved by topologists in the more general setting of (not necessarily zero-dimensional) compact spaces. An appendix demonstrates the application of advanced set-theoretic methods to the field. The intended readers are Boolean and universal algebraists. The book will also be useful for general topologists wanting to learn about kappa-metrizable spaces and related classes. The text is practically self-contained but assumes experience with the basic concepts and techniques of Boolean algebras. ... Read more

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The study of cardinal functions brings unity and depth to many investigations in the theory of Boolean algebras. Many of the functions have proved their importance in related fields in set theory or topology.

For the most important examples three general questions are considered: What is the relationship between various cardinal functions? How do they behave with respect to algebraic operations? What can one say about other cardinal functions naturally derived from a given one?

These notes provide a comprehensive survey of this area and include proofs for a large number of results. ... Read more

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During the last few decades the ideas, methods, and results ofthe theory of Boolean algebras have played an increasing role invarious branches of mathematics and cybernetics.
This monograph is devoted to the fundamentals of the theory of Booleanconstructions in universal algebra. Also considered are the problemsof presenting different varieties of universal algebra with theseconstructions, and applications for investigating the spectra andskeletons of varieties of universal algebras.
For researchers whose work involves universal algebra and logic.
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Boolean Algebras in Analysis consists of two parts. The first concerns the general theory at the beginner's level. Presenting classical theorems, the book describes the topologies and uniform structures of Boolean algebras, the basics of complete Boolean algebras and their continuous homomorphisms, as well as lifting theory. The first part also includes an introductory chapter describing the elementary to the theory.

The second part deals at a graduate level with the metric theory of Boolean algebras at a graduate level. The covered topics include measure algebras, their sub algebras, and groups of automorphisms. Ample room is allotted to the new classification theorems abstracting the celebrated counterparts by D.Maharam, A.H. Kolmogorov, and V.A.Rokhlin.

Boolean Algebras in Analysis is an exceptional definitive source on Boolean algebra as applied to functional analysis and probability. It is intended for all who are interested in new and powerful tools for hard and soft mathematical analysis.

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High Quality Content by WIKIPEDIA articles! In Boolean algebra, any Boolean function can be expressed in a canonical form using the dual concepts of minterms and maxterms. Minterms are called products because they are the logical AND of a set of variables, and maxterms are called sums because they are the logical OR of a set of variables (further definition appears in the sections headed Minterms and Maxterms below). These concepts are called duals because of their complementary-symmetry relationship as expressed by De Morgan's laws, which state that AND(x,y,z,...) = NOR(x',y',z',...) and OR(x,y,z,...) = NAND(x',y',z',...) (the apostrophe ' is an abbreviation for logical NOT, thus " x' " represents " NOT x ", the Boolean usage " x'y + xy' " represents the logical equation " (NOT(x) AND y) OR (x AND NOT(y)) "). The dual canonical forms of any Boolean function are a "sum of minterms" and a "product of maxterms." The term "Sum of Products" or "SoP" is widely used for the canonical form that is a disjunction (OR) of minterms. Its De Morgan dual is a "Product of Sums" or "PoS" for the canonical form that is a conjunction (AND) of maxterms. ... Read more

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This book describes the latest Russian research covering thestructure and algorithmic properties of Boolean algebras from thealgebraic and model-theoretic points of view. A significantly revisedversion of the author'sCountable Boolean Algebras(Nauka,Novosibirsk, 1989), the text presents new results as well as aselection of open questions on Boolean algebras. Other currentfeatures include discussions of the Kottonen algebras in enrichmentsby ideals and automorphisms, and the properties of the automorphismgroups. ... Read more