Narrow your search
Listing 1 - 3 of 3
Sort by

Book
Cardinal functions in topology ten years later
Author:
ISBN: 9061961963 Year: 1980 Volume: 123 Publisher: Amsterdam


Book
Cardinal Invariants on Boolean Algebras : Second Revised Edition
Author:
ISBN: 3034807295 3034807309 Year: 2014 Publisher: Basel : Springer Basel : Imprint: Birkhäuser,

Loading...
Export citation

Choose an application

Bookmark

Abstract

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.

Set theory : an introduction to large cardinals
Author:
ISBN: 0720422728 9780080954837 0080954839 9780080955025 0080955029 9780080954868 0080954863 1283525607 9781283525602 9786613838056 6613838055 9780080955087 0080955088 9780080570587 0080570585 9780444104779 0444104771 0720422000 9780720422726 9780720422009 9780444105356 0444105352 0720422795 9780720422795 9780444854018 0444854010 0444868399 9780444868398 0444851631 9780444851635 9786613837998 1283525542 9786613837868 1283525410 Year: 1974 Volume: v. 76 Publisher: Amsterdam : New York : North-Holland Pub. Co. ; American Elsevier Pub. Co.,

Loading...
Export citation

Choose an application

Bookmark

Abstract

Provability, Computability and Reflection

Keywords

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.

Listing 1 - 3 of 3
Sort by