The higher infinite : large cardinals in set theory from their beginnings
The higher infinite : large cardinals in set theory from their beginnings
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更高的无限：集合论中的大基数从一开始
DOI：
10.5860/choice.33-2791
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发表时间：
2005
影响因子：
0.3
通讯作者：
A. Kanamori
中科院分区：
文献类型：
--
作者：
A. Kanamori
大基数理论是现代集合论的一个主流，是分析数学命题的相对一致性和可能的数学新公理的主要研究领域。第一个计划的多卷系列，这本书提供了一个全面的帐户，从它的开始和一些直接的结果导致当代研究的前沿大红衣主教的理论。采用“遗传”方法，在其历史发展的背景下呈现主题。有了后见之明，相应的途径被追求，并给出最优雅或最容易理解的解释。通过提供开放的问题和推测，读者不仅可以欣赏整个企业的范围和一致性，而且可以通过研究相关章节准备在几个特定领域进行研究。
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.