This handbook is the definitive compendium of the methods, results, and current initiatives in modern set theory in all its research directions. Set theory has entered its prime as an advanced and autonomous field of mathematics with foundational significance, and the expanse and variety of this handbook attests to the richness and sophistication of the subject. The chapters are written by acknowledged experts, major research figures in their areas, and they each bring to bear their experience and insights in carefully wrought, self-contained expositions. There is historical depth, elegant development, probing to the frontiers, and prospects for the future. This handbook is essential reading for the aspiring researcher, a pivotal focus for the veteran set theorist, and a massive reference for all those who want to gain a larger sense of the tremendous advances that have been made in the subject, one which first appeared as a foundation of mathematics but in the last several decades has expanded into a broad and far-reaching field with its own self-fueling initiatives.
Author(s): Akihiro Kanamori (auth.), Matthew Foreman, Akihiro Kanamori (eds.)
Edition: 1
Publisher: Springer Netherlands
Year: 2010
Language: English
Pages: 2196
Tags: Mathematical Logic and Foundations; Logic; Philosophy of Science
Front Matter....Pages I-XIV
Introduction....Pages 1-92
Stationary Sets....Pages 93-128
Partition Relations....Pages 129-213
Coherent Sequences....Pages 215-296
Borel Equivalence Relations....Pages 297-332
Proper Forcing....Pages 333-394
Combinatorial Cardinal Characteristics of the Continuum....Pages 395-489
Invariants of Measure and Category....Pages 491-555
Constructibility and Class Forcing....Pages 557-604
Fine Structure....Pages 605-656
Σ * Fine Structure....Pages 657-736
Elementary Embeddings and Algebra....Pages 737-774
Iterated Forcing and Elementary Embeddings....Pages 775-883
Ideals and Generic Elementary Embeddings....Pages 885-1147
Cardinal Arithmetic....Pages 1149-1227
Successors of Singular Cardinals....Pages 1229-1350
Prikry-Type Forcings....Pages 1351-1447
Beginning Inner Model Theory....Pages 1449-1495
The Covering Lemma....Pages 1497-1594
An Outline of Inner Model Theory....Pages 1595-1684
A Core Model Toolbox and Guide....Pages 1685-1751
Structural Consequences of AD....Pages 1753-1876
Determinacy in L (ℝ)....Pages 1877-1950
Large Cardinals from Determinacy....Pages 1951-2119
Forcing over Models of Determinacy....Pages 2121-2177
Back Matter....Pages 2179-2197
