The Higher Infinite: Large Cardinals in Set Theory from Their Beginnings / Edition 2

The Higher Infinite: Large Cardinals in Set Theory from Their Beginnings / Edition 2

by Akihiro Kanamori, A. Kanamori
     
 

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ISBN-10: 3540003843

ISBN-13: 9783540003847

Pub. Date: 07/29/2003

Publisher: Springer-Verlag New York, LLC

This is the softcover reprint of the very popular hardcover edition. The theory of large cardinals is currently a broad mainstream of modern set theory, the main area of investigation for the analysis of the relative consistency of mathematical propositions and possible new axioms for mathematics. The first of a projected multi-volume series, this book provides a

Overview

This is the softcover reprint of the very popular hardcover edition. The theory of large cardinals is currently a broad mainstream of modern set theory, the main area of investigation for the analysis of the relative consistency of mathematical propositions and possible new axioms for mathematics. The first of a projected multi-volume series, this book provides a comprehensive account of the theory of large cardinals from its beginnings and some of the direct outgrowths leading to the frontiers of contemporary research. A "genetic" approach is taken, presenting the subject in the context of its historical development. With hindsight the consequential avenues are pursued and the most elegant or accessible expositions given. With open questions and speculations provided throughout the reader should not only come to appreciate the scope and coherence of the overall enterprise but also become prepared to pursue research in several specific areas by studying the relevant sections.

Product Details

ISBN-13:
9783540003847
Publisher:
Springer-Verlag New York, LLC
Publication date:
07/29/2003
Series:
Springer Monographs in Mathematics
Edition description:
REV
Pages:
564
Product dimensions:
6.14(w) x 9.21(h) x 1.31(d)

Table of Contents

Introduction XI

0 Preliminaries 1

Chapter 1 Beginnings

1 Inaccessibility 16

2 Measurability 22

3 Constructibility 28

4 Compactness 36

5 Elementary Embeddings 44

6 Indescribability 57

Chapter 2 Partition Properties

7 Partitions and Trees 70

8 Partitions and Structures 85

9 Indiscernibles and 0# 99

Chapter 3 Forcing and Sets of Reals

10 Development of Forcing 114

11 Lebesgue Measurability 132

12 Descriptive Set Theory 145

13 II 1 Sets and &stigma;12 Sets 162

14 Σ12 Sets and Sharps 178

15 Sharps and Σ1 3 Sets 192

Chapter 4 Aspects of Measurability

16 Saturated Ideals I 210

17 Saturated Ideals II 220

18 Prikry Forcing 234

19 Iterated Ultrapowers 244

20 Inner Models of Measurability 261

21 Embeddings, 0#, and 0&dag; 277

Chapter 5 Strong Hypotheses

22 Supercompactness 298

23 Extendibility to Inconsistency 311

24 The Strongest Hypotheses 325

25 Combinatorics of Pκγ 340

26 Extenders 352

Chapter 6 Determinacy

27 Infinite Games 368

28 AD and Combinatorics 383

29 Prewellorderings 403

30 Scales and Projective Ordinals 417

31 Det(α-II11) 437

32 Consistency of AD 450

Chart of Cardinals 472

Appendix 473

Indexed References 483

Subject Index 531

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