卡那莫里所著的《高阶无限(第2版)(英文版)》是一部很好的参考书籍,引用量相当高,可以说是关于大基数的写得最好的一本书。经过长期实践检验,本书已经变成集合论方面的一本标准参考书和引导教程。从头开始讲述大基数理论,一些直接结果引领了当代研究的前沿,并且附有一些开放性问题和前瞻性成果。
Introduction
0.Preliminaries
Chapter l.Beginnings
1.Inaccessibilit
2.Measurability
3.Constructibility
4.Compactness
5.Elementary Embeddings
6.Indescribability
Chapter 2.Partition Properties
7.Partitions and Trees
8.Partitions and Structures
9.Indiscernibles and 0#
Chapter 3.Forcing and Sets of Reals
10.Development of Forcing
11.Lebesgue Measurability
12.Descriptive Set Theory
13.Ⅱ1/1{Sets and∑1/2;Sets
14.∑1/2Sets and Sharps
15.Sharps and∑1/3;Sets
Chapter 4.Aspects of Measurability
16.Saturated Ideals Ⅰ
17.Saturated Ideals Ⅱ
18.Prikry Forcin9
19.Iterated Ultrapowers
20.Inner Models of Measurability
21.Embeddings, 0#, and 0t
Chapter 5. Strong Hypotheses
22.Supercompactness
23.Extendibility to Inconsistency
24.The Strongest Hypotheses
25.Combinatorics of Pxy
26.Extenders
Chapter 6. Determinacy
27.Infinite Games
28.AD and Combinatorics
29.Prewellorderings
30.Scales and Projective Ordinals
31.Det(ot-lll)
32.Consistency of AD
Chart of Cardinals
Appendix
Indexed References
Subject Index