Hardcover ISBN:  9780821805282 
Product Code:  GSM/18 
224 pp 
List Price:  $51.00 
MAA Member Price:  $45.90 
AMS Member Price:  $40.80 
Electronic ISBN:  9781470420758 
Product Code:  GSM/18.E 
224 pp 
List Price:  $48.00 
MAA Member Price:  $43.20 
AMS Member Price:  $38.40 

Book DetailsGraduate Studies in MathematicsVolume: 18; 1997MSC: Primary 03;
This is the second volume of a twovolume graduate text in set theory. The first volume covered the basics of modern set theory and was addressed primarily to beginning graduate students. This second volume is intended as a bridge between introductory set theory courses and advanced monographs that cover selected branches of set theory, such as forcing or large cardinals. The authors give short but rigorous introductions to settheoretic concepts and techniques such as trees, partition calculus, cardinal invariants of the continuum, Martin's Axiom, closed unbounded and stationary sets, the Diamond Principle (\(\diamond\)), and the use of elementary submodels. Great care has been taken to motivate the concepts and theorems presented.
The book is written as a dialogue with the reader. The presentation is interspersed with numerous exercises. The authors wish to entice readers into active participation in discovering the mathematics presented, making the book particularly suitable for selfstudy. Each topic is presented rigorously and in considerable detail. Carefully planned exercises lead the reader to active mastery of the techniques presented. Suggestions for further reading are given. Volume II can be read independently of Volume I.ReadershipGraduate students and research mathematicians interested in set theory; researchers who want to learn how to use settheoretic tools, such as Martin's Axiom, the Diamond Principle, and closed unbounded and stationary sets.

Table of Contents

Chapters

Chapter 13. Filters and ideals in partial orders

Chapter 14. Trees

Chapter 15. A little Ramsey theory

Chapter 16. The $\Delta $system lemma

Chapter 17. Applications of the Continuum Hypothesis

Chapter 18. From the RasiowaSikorski Lemma to Martin’s Axiom

Chapter 19. Martin’s Axiom

Chapter 20. Hausdorff gaps

Chapter 21. Closed unbounded sets and stationary sets

Chapter 22. The $\lozenge $principle

Chapter 23. Measurable cardinals

Chapter 24. Elementary submodels

Chapter 25. Boolean algebras

Chapter 26. Appendix: Some general topology


Additional Material

Reviews

[The book is] thoughtfully written, and offers a large number of exercises. [It] can serve as an appetizer for many subfields of set theory; the authors not only give proofs of many of the classical theorems, but also do an excellent job of motivating theorems and definitions. The “mathographical remarks” at the end of each chapter contain points to textbooks, monographs and surveys, or sometimes even to research papers that are accessible to all who have read and understood [this book]. Through the exercises placed in the text, the authors have done an excellent job of synchronizing the students' thoughts with their own–after finishing an exercise the student is ready for the next definition, theorem, or example. [The book is] highly informative, a pleasure to read, and can be warmly recommended.
Journal of Symbolic Logic 
As a text for a second semester in set theory, it is excellent …
Mathematical Reviews


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This is the second volume of a twovolume graduate text in set theory. The first volume covered the basics of modern set theory and was addressed primarily to beginning graduate students. This second volume is intended as a bridge between introductory set theory courses and advanced monographs that cover selected branches of set theory, such as forcing or large cardinals. The authors give short but rigorous introductions to settheoretic concepts and techniques such as trees, partition calculus, cardinal invariants of the continuum, Martin's Axiom, closed unbounded and stationary sets, the Diamond Principle (\(\diamond\)), and the use of elementary submodels. Great care has been taken to motivate the concepts and theorems presented.
The book is written as a dialogue with the reader. The presentation is interspersed with numerous exercises. The authors wish to entice readers into active participation in discovering the mathematics presented, making the book particularly suitable for selfstudy. Each topic is presented rigorously and in considerable detail. Carefully planned exercises lead the reader to active mastery of the techniques presented. Suggestions for further reading are given. Volume II can be read independently of Volume I.
Graduate students and research mathematicians interested in set theory; researchers who want to learn how to use settheoretic tools, such as Martin's Axiom, the Diamond Principle, and closed unbounded and stationary sets.

Chapters

Chapter 13. Filters and ideals in partial orders

Chapter 14. Trees

Chapter 15. A little Ramsey theory

Chapter 16. The $\Delta $system lemma

Chapter 17. Applications of the Continuum Hypothesis

Chapter 18. From the RasiowaSikorski Lemma to Martin’s Axiom

Chapter 19. Martin’s Axiom

Chapter 20. Hausdorff gaps

Chapter 21. Closed unbounded sets and stationary sets

Chapter 22. The $\lozenge $principle

Chapter 23. Measurable cardinals

Chapter 24. Elementary submodels

Chapter 25. Boolean algebras

Chapter 26. Appendix: Some general topology

[The book is] thoughtfully written, and offers a large number of exercises. [It] can serve as an appetizer for many subfields of set theory; the authors not only give proofs of many of the classical theorems, but also do an excellent job of motivating theorems and definitions. The “mathographical remarks” at the end of each chapter contain points to textbooks, monographs and surveys, or sometimes even to research papers that are accessible to all who have read and understood [this book]. Through the exercises placed in the text, the authors have done an excellent job of synchronizing the students' thoughts with their own–after finishing an exercise the student is ready for the next definition, theorem, or example. [The book is] highly informative, a pleasure to read, and can be warmly recommended.
Journal of Symbolic Logic 
As a text for a second semester in set theory, it is excellent …
Mathematical Reviews