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Set Theory

Set Theory

$79.99

Part of London Mathematical Society Student Texts

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

$79.99
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  • This is a classic introduction to set theory, suitable for students with no previous knowledge of the subject. Providing complete, up-to-date coverage, the book is based in large part on courses given over many years by Professor Hajnal. The first part introduces all the standard notions of the subject; the second part concentrates on combinatorial set theory. Exercises are included throughout and a new section of hints has been added to assist the reader.

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

    "The great number of exercises and problems (some of them with hints for solution) makes this book a valuable text for mathematics majors and also for an undergraduate course in mathematical logic." Monatshefte fur Mathematik

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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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