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Basic Set Theoryby Azriel Levy
Synopses & ReviewsPublisher Comments:Although this book deals with basic set theory (in general, it stops short of areas where modeltheoretic methods are used) on a rather advanced level, it does it at an unhurried pace. This enables the author to pay close attention to interesting and important aspects of the topic that might otherwise be skipped over. Written for upperlevel undergraduate and graduate students, the book is divided into two parts. The first covers pure set theory, including the basic notions, order and wellfoundedness, cardinal numbers, the ordinals, and the axiom of choice and some of its consequences. The second part deals with applications and advanced topics, among them a review of point set topology, the real spaces, Boolean algebras, and infinite combinatorics and large cardinals. A helpful appendix deals with eliminability and conservation theorems, while numerous exercises supply additional information on the subject matter and help students test their grasp of the material. 1979 edition. 20 figures. Book News Annotation:This advanced mathematics textbook introduces the theorems and proofs of cardinal numbers, the ordinals, the axiom of choice, the space of real numbers, Boolean algebras, trees, and partitions. Originally published by Springer Verlag in 1979, this reprint adds an appendix of corrections.
Annotation c. Book News, Inc., Portland, OR (booknews.com) Synopsis:The first part of this advancedlevel text covers pure set theory, and the second deals with applications and advanced topics (point set topology, real spaces, Boolean algebras, infinite combinatorics and large cardinals). 1979 edition. Synopsis:An advancedlevel treatment of the basics of set theory, this text offers students a firm foundation, stopping just short of the areas employing modeltheoretic methods. Geared toward upperlevel undergraduate and graduate students, it consists of two parts: the first covers pure set theory, including the basic motions, order and wellfoundedness, cardinal numbers, the ordinals, and the axiom of choice and some of it consequences; the second deals with applications and advanced topics such as point set topology, real spaces, Boolean algebras, and infinite combinatorics and large cardinals. An appendix comprises useful information on eliminability and conservation theorems, and numerous exercises help students test their grasp of each topic. 1979 edition. 20 figures. Table of ContentsPart A. Pure Set Theory
and#160; Chapter I. The Basic Notions and#160;and#160;and#160; 1. The Basic Language of Set Theory and#160;and#160;and#160; 2. The Axioms of Extensionality and Comprehension and#160;and#160;and#160; 3. Classes, Why and How and#160;and#160;and#160; 4. Classes, the formal Introduction and#160;and#160;and#160; 5. The Axioms of Set Theory and#160;and#160;and#160; 6. Relations and functions and#160; Chapter II. Order and WellFoundedness and#160;and#160;and#160; 1. Order and#160;and#160;and#160; 2. WellOrder and#160;and#160;and#160; 3. Ordinals and#160;and#160;and#160; 4. Natural Numbers and finite Sequences and#160;and#160;and#160; 5. WellFounded Relations and#160;and#160;and#160; 6. WellFounded Sets and#160;and#160;and#160; 7. The Axiom of Foundation and#160; Chapter III. Cardinal Numbers and#160;and#160;and#160; 1. Finite Sets and#160;and#160;and#160; 2. The Partial Order of the Cardinals and#160;and#160;and#160; 3. The Finite Arithmetic of the Cardinals and#160;and#160;and#160; 4. The Infinite Arithmetic of the Well Orderd Cardinals and#160; Chapter IV. The Ordinals and#160;and#160;and#160; 1. Ordinal Addition and Multiplication and#160;and#160;and#160; 2. Ordinal Exponentiation and#160;and#160;and#160; 3. Cofinality and Regular Ordinals and#160;and#160;and#160; 4. Closed Unbounded Classes and Stationery Classes and#160; Chapter V. The Axiom of Choice and Some of Its Consequences and#160;and#160;and#160; 1. The Axiom of Choice and Equivalent Statements and#160;and#160;and#160; 2. Some Weaker Versions of the Axiom of Choice and#160;and#160;and#160; 3. Definable Sets and#160;and#160;and#160; 4. Set Theory with Global Choice and#160;and#160;and#160; 5. Cardinal Exponentiation Part B. Applications and Advanced Topics and#160; Chapter VI. A Review of Point Set Topology and#160;and#160;and#160; 1. Basic concepts and#160;and#160;and#160; 2. Useful Properties and Operations and#160;and#160;and#160; 3. Category, Baire and Borel Sets and#160; Chapter VII. The Real Spaces and#160;and#160;and#160; 1. The Real Numbers and#160;and#160;and#160; 2. The Separable Complete Metric Spaces and#160;and#160;and#160; 3. The Close Relationship Between the Real Numbers, the Cantor Space and the Baire Space and#160; Chapter VIII. Boolean Algebras and#160;and#160;and#160; 1. The Basic Theory and#160;and#160;and#160; 2. Prime Ideals and Representation and#160;and#160;and#160; 3. Complete Boolean Algebras and#160;and#160;and#160; 4. Martin's Axiom and#160; Chapter IX. Infinite Combinatorics and Large Cardinals and#160;and#160;and#160; 1. The Axiom of Constructibility and#160;and#160;and#160; 2. Trees and#160;and#160;and#160; 3. Partition Properties and#160;and#160;and#160; 4. Measurable Cardinals Appendix X. The Eliminability and Conservation Theorems and#160; Bibliography; Additional Bibliography; Index of Notation; Index Appendix Corrections and Additions What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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