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This item may be Check for Availability Other titles in the Pure and Applied Mathematics: A WileyInterscience Series of Texts, Monographs and Tracts series:
Introduction to Modern Set Theory (Pure and Applied Mathematics: A WileyInterscience Series of Texts, Monographs and Tracts)
Synopses & ReviewsPublisher Comments:This is modern set theory from the ground upfrom partial orderings and wellordered sets to models, infinite cobinatorics and large cardinals. The approach is unique, providing rigorous treatment of basic settheoretic methods, while integrating advanced material such as independence results, throughout. The presentation incorporates much interesting historical material and no background in mathematical logic is assumed. Treatment is selfcontained, featuring theorem proofs supported by diagrams, examples and exercises. Includes applications of set theory to other branches of mathematics.
Table of ContentsSome Mathematical Preliminaries.
Partially Ordered Sets. Some Facts About Partially Ordered Sets. Equivalence Relations. WellOrdered Sets. Mathematical Induction. Models. THE AXIOMS, PART I. The Language, Some Finite Operations, and Extensionality. Pairs. Cartesian Products. Union, Intersection, and Separation. Filters and Ideas. The Natural Numbers. Two Nonconstructive Axioms: Infinity and Power Set. A Digression on the Power Set Axiom. Replacement. REGULARITY AND CHOICE. Transitive Sets. A First Look at Ordinals. Regularity. A World About Classes. The Axiom of Choice. Four Forms of the Axiom of Choice. Models of Regularity and Choice. THE FOUNDATION OF MATHEMATICS. INFINITE NUMBERS. Cardinality. Ordinal Arithmetic. Cardinal Arithmetic. Cofinality. Infinite Operations and More Exponentiation. Counting. TWO MODELS OF SET THEORY. A Set Model for ZFC. The Constructible Universe. INFINITE COMBINATORICS. Partition Calculus. Trees. Measurable Cardinals. CH. Martin's Axiom. Stationary Sets. Bibliography. Index. What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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Humanities » Philosophy » Logic


