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Handbook of Set Theory

  • Book
  • © 2010

Overview

Editors:
  1. Matthew Foreman

    1. School of Physical Sciences, University of California, Irvine, Irvine, U.S.A.

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    You can also search for this editor in PubMed   Google Scholar

  2. Akihiro Kanamori

    1. Dept. Manufacturing Engineering, Boston University, Boston, U.S.A.

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  • Definitive compendium of all of modern set theory
  • Chapters written by the leading experts in their areas
  • Carefully crafted, self-contained expositions for all the subfields of set theory
  • No other up-to-date single source available for all the subfields of set theory
  • Includes supplementary material: sn.pub/extras

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Table of contents (25 chapters)

  1. Front Matter

    Pages I-XIV
    Download chapter PDF

  2. Introduction

    • Akihiro Kanamori
    Pages 1-92

  3. Stationary Sets

    • Thomas Jech
    Pages 93-128

  4. Partition Relations

    • András Hajnal, Jean A. Larson
    Pages 129-213

  5. Coherent Sequences

    • Stevo Todorcevic
    Pages 215-296

  6. Borel Equivalence Relations

    • Greg Hjorth
    Pages 297-332

  7. Proper Forcing

    • Uri Abraham
    Pages 333-394

  8. Combinatorial Cardinal Characteristics of the Continuum

    • Andreas Blass
    Pages 395-489

  9. Invariants of Measure and Category

    • Tomek Bartoszynski
    Pages 491-555

  10. Constructibility and Class Forcing

    • Sy D. Friedman
    Pages 557-604

  11. Fine Structure

    • Ralf Schindler, Martin Zeman
    Pages 605-656

  12. Σ* Fine Structure

    • Philip D. Welch
    Pages 657-736

  13. Elementary Embeddings and Algebra

    • Patrick Dehornoy
    Pages 737-774

  14. Iterated Forcing and Elementary Embeddings

    • James Cummings
    Pages 775-883

  15. Ideals and Generic Elementary Embeddings

    • Matthew Foreman
    Pages 885-1147

  16. Cardinal Arithmetic

    • Uri Abraham, Menachem Magidor
    Pages 1149-1227

  17. Successors of Singular Cardinals

    • Todd Eisworth
    Pages 1229-1350

  18. Prikry-Type Forcings

    • Moti Gitik
    Pages 1351-1447

  19. Beginning Inner Model Theory

    • William J. Mitchell
    Pages 1449-1495

  20. The Covering Lemma

    • William J. Mitchell
    Pages 1497-1594
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Keywords

About this book

Numbers imitate space, which is of such a di?erent nature —Blaise Pascal It is fair to date the study of the foundation of mathematics back to the ancient Greeks. The urge to understand and systematize the mathematics of the time led Euclid to postulate axioms in an early attempt to put geometry on a ?rm footing. With roots in the Elements, the distinctive methodology of mathematics has become proof. Inevitably two questions arise: What are proofs? and What assumptions are proofs based on? The ?rst question, traditionally an internal question of the ?eld of logic, was also wrestled with in antiquity. Aristotle gave his famous syllogistic s- tems, and the Stoics had a nascent propositional logic. This study continued with ?ts and starts, through Boethius, the Arabs and the medieval logicians in Paris and London. The early germs of logic emerged in the context of philosophy and theology. The development of analytic geometry, as exempli?ed by Descartes, ill- tratedoneofthedi?cultiesinherentinfoundingmathematics. Itisclassically phrased as the question ofhow one reconciles the arithmetic with the geom- ric. Arenumbers onetypeofthingand geometricobjectsanother? Whatare the relationships between these two types of objects? How can they interact? Discovery of new types of mathematical objects, such as imaginary numbers and, much later, formal objects such as free groups and formal power series make the problem of ?nding a common playing ?eld for all of mathematics importunate. Several pressures made foundational issues urgent in the 19th century.

Reviews

From the reviews:

“This Handbook is written for graduate students and researchers … . The 24 chapters and a long introduction are written by acknowledged experts, major research figures in their areas. … The Handbook is completed by an extensive Index.”­­­ (Martin Weese, Zentralblatt MATH, Vol. 1197, 2010)

Editors and Affiliations

  • School of Physical Sciences, University of California, Irvine, Irvine, U.S.A.

    Matthew Foreman

  • Dept. Manufacturing Engineering, Boston University, Boston, U.S.A.

    Akihiro Kanamori

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