高階無限 第2版

內(nèi)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.

書籍目錄

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

章節(jié)摘錄

　　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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