Handbook of Set Theory

1. Front Matter

   Pages I-XIV

   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

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.

• Arithmetic
• Combinatorics
• Continuum
• Determinacy
• Equivalence
• Large Cardinals
• Lemma
• cardinals
• set theory

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)

• 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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