Introduction to Modern Set Theory
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品牌: Judith Roitman
基本信息出版社:Wiley-Interscience; 1 (1990年1月16日)丛书名:Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts精装:176页正文语种:英语ISBN:0471635197条形码:9780471635192商品尺寸:16.1 x 1.6 x 24.2 cm商品重量:422 gASIN:0471635197商品描述内容简介This is modern set theory from the ground up--from partial orderings and well-ordered sets to models, infinite cobinatorics and large cardinals. The approach is unique, providing rigorous treatment of basic set-theoretic 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 self-contained, featuring theorem proofs supported by diagrams, examples and exercises. Includes applications of set theory to other branches of mathematics.目录Some Mathematical Preliminaries.
Partially Ordered Sets.
Some Facts About Partially Ordered Sets.
Equivalence Relations.
Well-Ordered 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.