高阶无限 第2版

出版时间:2011-6  出版社:世界图书出版公司  作者:卡那莫里  页数:536  
Tag标签:无  

内容概要

  My first thanks goes to Gert Miiller who initially suggested this project and persisted in its encouragement. Thanks also to Thomas Orowan who went through many iterations of the difficult typing in the early stages. James Baumgartner,Howard Becket, and Jose Ruiz read through large portions of the text and offered extensive suggestions.

书籍目录

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
 ……
Subject Index

章节摘录

  First, the various hypotheses though arising from diverse motivations and historical happenstance nonetheless form a linear hierarchy, one neatly delimited by Kunen's inconsistency result. Typically for two large cardinal hypotheses, below a cardinal satisfying one there are many cardinals satisfying the other, in a sense prescribed by the first.Moreover, the weaker hypotheses through strong forms of measurability have been bolstered by a variety of equiconsistency results involving combinatorial proposi-tions low in the cumulative hierarchy. In this respect, particularly intriguing is the work on the Singular Cardinals Problem, which showed that something as basic as rendering 2" large for singular strong iimit cardinals K essentially requires large cardinals. Finally, a variety of strong propositions have been informatively brack-eted in consistency strength between two large cardinal hypotheses: The stronger hypothesis implies that there is a forcing extension in which the proposition ob-tains; and if the proposition obtains, there is an inner model satisfying the weaker hypothesis. Supercompactness has often figured as the upper bound, but some-times n-hugeness and even the hypotheses just short of Kunen's inconsistency have played this role. (This wide-ranging exploration is the subject of volume II.)   ……

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用户评论 (总计2条)

 
 

  •   本书是SMM(斯普林格数学专著)系列的一本,讲集合论。当然SMM很专业的啦,建议先看耶哈那本再看这个。这里面起点比较高。
  •   Kanamori 的这本书与其说是数学,不如说更多是集合论中大基数这一分支的历史。当然这是一段精彩的故事。可惜世界出版社还是保留以往官方盗版商的气质,纸质差,装订差,还有印刷模糊的页面。好在有电子版,不想费功夫换了。
 

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