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Fast Track to Forcing

Fast Track to Forcing

Fast Track to Forcing

Mirna Džamonja, Institute for the History and Philosophy of Science and Technology, Paris
October 2020
Paperback
9781108413145

    This quick yet detailed introduction to set theory and forcing builds the reader's intuition about it as much as the mathematical detail. Intuition, rather absent from the existing literature on the subject, here plays a large role. The reader will not only learn the facts, but will understand why they are true and will be brought to ask: what else could be true? Having presented forcing in Part I, the second part of the book discusses contemporary issues in the theory of forcing. It includes known and some previously unpublished results as well as many open questions. This is ideal for those who want to start a research career in forcing but do not have a personal interlocutor. Obviously, not everything about forcing is in this book. Many references are included to help the reader further explore the vast amount of research literature available on the subject.

    • A sleek introduction to the theory of forcing, which allows even those who do not have any background in set theory to understand the subject
    • Devotes the second part of the book to contemporary topics in the theory of forcing, including open questions
    • Includes previously unpublished results in the theory of forcing

    Reviews & endorsements

    '… a rare book written for non-specialists that describes recent developments in set theory without assuming any knowledge. It will be an excellent resource for people who want to know current research in this field.' Tetsuya Ishiu, zbMATH Open

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    Product details

    October 2020
    Paperback
    9781108413145
    200 pages
    230 × 153 × 10 mm
    0.25kg
    Available

    Table of Contents

    • Part I. Let's Be Independent:
    • 1. Introduction
    • 2. Axiomatic Systems
    • 3. Zermelo-Fraenkel Axioms and the Axiom of Choice
    • 4. Well Orderings and Ordinals
    • 5. Cardinals
    • 6. Models and Independence
    • 7. Some Class Models of ZFC
    • 8. Forcing
    • 9. Violating CH
    • Part II. What Is New in Set Theory:
    • 10. Introduction to Part Two
    • 11. Classical Extensions
    • 12. Iterated Forcing and Martin's Axiom
    • 13. Some More Large Cardinals
    • 14. Limitations of Martin's Axiom and Countable Supports
    • 15. Proper Forcing and PFA
    • 16. $aleph_2$ and other Successors of Regulars
    • 17. Singular Cardinal Hypothesis and some PCF
    • 18. Forcing at Singular Cardinals and their Successors
    • References
    • Index.