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Topology --- Functions --- Cardinal numbers --- Fonctions (Mathématiques) --- Nombres cardinaux --- Topologie --- 510.2 --- Numbers, Cardinal --- Arithmetic, Cardinal --- Cardinal arithmetic --- Cardinals (Numbers) --- Set theory --- Transfinite numbers --- Analysis (Mathematics) --- Differential equations --- Mathematical analysis --- Mathematics --- Numbers, Complex --- Calculus --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Algebras, Linear --- Foundations of mathematics --- 510.2 Foundations of mathematics --- Fonctions (Mathématiques)
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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 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 185 are formulated. Based on Cardinal Functions on Boolean Algebras (1990) and Cardinal Invariants on Boolean Algebras (1996) by the same author, the present work is much larger than either of these. It contains solutions to many of the open problems of the earlier volumes. Among the new topics are continuum cardinals on Boolean algebras, with a lengthy treatment of the reaping number. Diagrams at the end of the book summarize the relationships between the functions for many important classes of Boolean algebras, including interval algebras, tree algebras and superatomic algebras.
Algebra, Boolean --- Functions --- Cardinal numbers --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Algebra, Boolean. --- Functions. --- Cardinal numbers. --- Arithmetic, Cardinal --- Cardinal arithmetic --- Cardinals (Numbers) --- Numbers, Cardinal --- Analysis (Mathematics) --- Boolean algebra --- Boole's algebra --- Mathematics. --- Algebra. --- Ordered algebraic structures. --- Mathematical logic. --- Mathematical Logic and Foundations. --- Order, Lattices, Ordered Algebraic Structures. --- Set theory --- Transfinite numbers --- Differential equations --- Mathematical analysis --- Numbers, Complex --- Calculus --- Algebraic logic --- Logic, Symbolic and mathematical. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Syllogism --- Algebraic structures, Ordered --- Structures, Ordered algebraic --- Algebra
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Provability, Computability and Reflection
Mathematical logic --- Algebraic logic --- Logique algébrique --- Algebra, Boolean --- Boole, Algèbre de --- Cylindric algebras --- Algèbres cylindriques. --- Set theory. --- Cardinal numbers. --- Arithmetic, Cardinal --- Cardinal arithmetic --- Cardinals (Numbers) --- Numbers, Cardinal --- Set theory --- Transfinite numbers --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Logic, Symbolic and mathematical --- Mathematics --- 510.22 --- 510.22 Set theory. Set theoretic approach. Theory of order types, of ordinal and cardinal numbers --- Set theory. Set theoretic approach. Theory of order types, of ordinal and cardinal numbers --- 510.64 --- 510.64 Non-classical, formal systems of logic. Modal logic. Multiple-value logics. Syllogistics. Inductive logic. Probabilistic logic --- Non-classical, formal systems of logic. Modal logic. Multiple-value logics. Syllogistics. Inductive logic. Probabilistic logic --- Recursion theory --- 510.6 --- 510.6 Mathematical logic --- Congresses --- Axiomatic set theory --- Axioms --- Congresses. --- Proof theory --- Logique algébrique --- Théorie de la preuve --- ELSEVIER-B EPUB-LIV-FT --- Cardinal numbers --- Théorie des ensembles --- Nombres cardinaux --- Théorie de la récursivité --- Congrès --- Théorie axiomatique des ensembles --- Axiomatic set theory. --- Logique mathématique. --- Récursivité, Théorie de la. --- Recursion theory - Congresses --- Numbers, cardinals --- Théorie des ensembles --- Logic, Symbolic and mathematical -- Periodicals. --- Logic, Symbolic and mathematical. --- Recursion theory - Congresses. --- Recursion theory -- Congresses. --- Physical Sciences & Mathematics --- Mathematical Theory --- Algebraic logic. --- Proof theory.
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