| 书目名称 | The Higher Infinite | | 副标题 | Large Cardinals in S | | 编辑 | Akihiro Kanamori | | 视频video | | | 概述 | Has become a standard reference and guide in the set theory community.Includes supplementary material: | | 丛书名称 | Springer Monographs in Mathematics | | 图书封面 |  | | 描述 | The higher in?nite refers to the lofty reaches of the in?nite cardinalities of set t- ory as charted out by large cardinal hypotheses. These hypotheses posit cardinals that prescribe their own transcendence over smaller cardinals and provide a sup- structure for the analysis of strong propositions. As such they are the rightful heirs to the two main legacies of Georg Cantor, founder of set theory: the extension of number into the in?nite and the investigation of de?nable sets of reals. The investigation of large cardinal hypotheses is indeed a mainstream of modern set theory, and they have been found to play a crucial role in the study of de?nable sets of reals, in particular their Lebesgue measurability. Although formulated at various stages in the development of set theory and with different incentives, the hypotheses were found to form a linear hierarchy reaching up to an inconsistent extension of motivating concepts. All known set-theoretic propositions have been gauged in this hierarchy in terms of consistency strength, and the emerging str- ture of implications provides a remarkably rich, detailed and coherent picture of the strongest propositions of mathematics as embedded i | | 出版日期 | Book 2003Latest edition | | 关键词 | cardinals; infinitary combinatorics; large cardinals; new axioms for set theory; relative consistency re | | 版次 | 2 | | doi | https://doi.org/10.1007/978-3-540-88867-3 | | isbn_softcover | 978-3-540-88866-6 | | isbn_ebook | 978-3-540-88867-3Series ISSN 1439-7382 Series E-ISSN 2196-9922 | | issn_series | 1439-7382 | | copyright | Springer-Verlag Berlin Heidelberg 2003 |
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发表于 2025-3-21 18:46:13
