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Titlebook: Combinatorial Set Theory; With a Gentle Introd Lorenz J. Halbeisen Book 20121st edition Springer-Verlag London Limited 2012 Axiom of Choice

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發(fā)表于 2025-3-21 20:09:02 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Combinatorial Set Theory
副標(biāo)題With a Gentle Introd
編輯Lorenz J. Halbeisen
視頻videohttp://file.papertrans.cn/231/230016/230016.mp4
概述Provides a comprehensive introduction to the sophisticated technique of forcing.Complete proofs of famous results are given, for instance, Robinson’s construction of doubling the unit ball using just
叢書名稱Springer Monographs in Mathematics
圖書封面Titlebook: Combinatorial Set Theory; With a Gentle Introd Lorenz J. Halbeisen Book 20121st edition Springer-Verlag London Limited 2012 Axiom of Choice
描述This book provides a self-contained introduction to modern set theory and also opens up some more advanced areas of current research in this field. The first part offers an overview of classical set theory wherein the focus lies on the axiom of choice and Ramsey theory. In the second part, the sophisticated technique of forcing, originally developed by Paul Cohen, is explained in great detail. With this technique, one can show that certain statements, like the continuum hypothesis, are neither provable nor disprovable from the axioms of set theory. In the last part, some topics of classical set theory are revisited and further developed in the light of forcing. The notes at the end of each chapter put the results in a historical context, and the numerous related results and the extensive list of references lead the reader to the frontier of research. This book will appeal to all mathematicians interested in the foundations of mathematics, but will be of particular use to graduates in this field.
出版日期Book 20121st edition
關(guān)鍵詞Axiom of Choice; Cardinal Characteristics of the Continuum; Combinatorics of Forcing; Consistency and I
版次1
doihttps://doi.org/10.1007/978-1-4471-2173-2
isbn_ebook978-1-4471-2173-2Series ISSN 1439-7382 Series E-ISSN 2196-9922
issn_series 1439-7382
copyrightSpringer-Verlag London Limited 2012
The information of publication is updating

書目名稱Combinatorial Set Theory影響因子(影響力)




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沙發(fā)
發(fā)表于 2025-3-21 22:31:24 | 只看該作者
1439-7382 frontier of research. This book will appeal to all mathematicians interested in the foundations of mathematics, but will be of particular use to graduates in this field.978-1-4471-2173-2Series ISSN 1439-7382 Series E-ISSN 2196-9922
板凳
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地板
發(fā)表于 2025-3-22 06:48:15 | 只看該作者
1439-7382 obinson’s construction of doubling the unit ball using just This book provides a self-contained introduction to modern set theory and also opens up some more advanced areas of current research in this field. The first part offers an overview of classical set theory wherein the focus lies on the axio
5#
發(fā)表于 2025-3-22 11:44:39 | 只看該作者
https://doi.org/10.1007/978-1-4020-8796-7ly Combinatorics is quite difficult to define. Nevertheless, let us start with a definition of Combinatorics which will be suitable for our purpose: . Below we give a few examples which should illustrate some aspects of infinitary Combinatorics. At the same time, we present the main topics of this book, which are the ., and ..
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https://doi.org/10.1007/978-3-7643-8266-7 in our counting the ninth axiom of .—states as follows:... Informally, every family of non-empty sets has a choice function, or equivalently, every Cartesian product of non-empty sets is non-empty..In this chapter, the .—as well as some weaker forms of it—will be discussed in great detail.
8#
發(fā)表于 2025-3-22 23:55:07 | 只看該作者
https://doi.org/10.1007/978-3-7643-8266-7s to the set of . of elements of . of a . function from . onto .. Similarly, .-element subsets of . correspond to images of injective functions from . into ., whereas .-block partitions of . correspond to pre-images of surjective functions from . onto .. Thus, to some extent, subsets of . and partitions of . are dual to each other.
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