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Set Theory

Set Theory

£53.99

Part of London Mathematical Society Student Texts

  • Date Published: November 1999
  • availability: Available
  • format: Paperback
  • isbn: 9780521596671

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  • This is a classic introduction to set theory in three parts. The first part gives a general introduction to set theory, suitable for undergraduates; complete proofs are given and no background in logic is required. Exercises are included, and the more difficult ones are supplied with hints. An appendix to the first part gives a more formal foundation to axiomatic set theory, supplementing the intuitive introduction given in the first part. The final part gives an introduction to modern tools of combinatorial set theory. This part contains enough material for a graduate course of one or two semesters. The subjects discussed include stationary sets, delta systems, partition relations, set mappings, measurable and real-valued measurable cardinals. Two sections give an introduction to modern results on exponentiation of singular cardinals, and certain deeper aspects of the topics are developed in advanced problems.

    • Extremely reader-friendly presentation
    • Fully class tested (in Hungary and the USA)
    • Contains a wealth of exercises
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    Reviews & endorsements

    'This is a classic introduction to set theory …'. L'Enseignement Mathématique

    'Give this book fifteen minutes attention - you will find that you must buy it! European Maths Society Journal

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    Product details

    • Date Published: November 1999
    • format: Paperback
    • isbn: 9780521596671
    • length: 328 pages
    • dimensions: 229 x 152 x 19 mm
    • weight: 0.48kg
    • availability: Available
  • Table of Contents

    Part I. Introduction to Set Theory:
    1. Notation, conventions
    2. Definition of equivalence. The concept of cardinality. The axiom of choice
    3. Countable cardinal, continuum cardinal
    4. Comparison of cardinals
    5. Operations with sets and cardinals
    6. Examples
    7. Ordered sets. Order types. Ordinals
    8. Properties of well-ordered sets. Good sets. The ordinal operation
    9. Transfinite induction and recursion
    10. Definition of the cardinality operation. Properties of cardinalities. The confinality operation
    11. Properties of the power operation
    Appendix. An axiomatic development of set theory
    Part II. Topics in Combinatorial Set Theory:
    12. Stationary sets
    13. Delta-systems
    14. Ramsey's theorem and its generalizations. Partition calculus
    15. Inaccessible cardinals. Mahlo cardinals
    16. Measurable cardinals
    17. Real-valued measurable cardinals, saturated ideas
    18. Weakly compact and Ramsey cardinals
    19. Set mappings
    20. The square-bracket symbol. Strengthenings of the Ramsey counterexamples
    21. Properties of the power operation
    22. Powers of singular cardinals. Shelah's theorem.

  • Authors

    Andras Hajnal, Rutgers University, New Jersey

    Peter Hamburger, Western Kentucky University

    Translator

    Attila Mate

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