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Titlebook: Combinatorial Set Theory; With a Gentle Introd Lorenz J. Halbeisen Book 2017Latest edition Springer International Publishing AG 2017 axiom

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發(fā)表于 2025-3-21 19:45:09 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書(shū)目名稱(chēng)Combinatorial Set Theory
副標(biāo)題With a Gentle Introd
編輯Lorenz J. Halbeisen
視頻videohttp://file.papertrans.cn/231/230015/230015.mp4
概述Provides a comprehensive introduction to the sophisticated technique of forcing.Includes Shelah’s astonishing construction of a model in which exactly 27 Ramsey ultrafilters exist.Offers topics and op
叢書(shū)名稱(chēng)Springer Monographs in Mathematics
圖書(shū)封面Titlebook: Combinatorial Set Theory; With a Gentle Introd Lorenz J. Halbeisen Book 2017Latest edition Springer International Publishing AG 2017 axiom
描述This book, now in a thoroughly revised second edition, provides a comprehensive and accessible introduction to modern set theory..Following an overview of basic notions in combinatorics and first-order logic, the author outlines the main topics of classical set theory in the second part, including Ramsey theory and the axiom of choice. The revised edition contains new permutation models and recent results in set theory without the axiom of choice. The third part explains the sophisticated technique of forcing in great detail, now including a separate chapter on Suslin’s problem. The technique is used to show that certain statements are neither provable nor disprovable from the axioms of set theory. In the final part, some topics of classical set theory are revisited and further developed in light of forcing, with new chapters on Sacks Forcing and Shelah’s astonishing construction of a model with finitely many Ramsey ultrafilters..Written for graduate students in axiomatic set theory, .Combinatorial Set Theory. will appeal to all researchers interested in the foundations of mathematics. With extensive reference lists and historical remarks at the end of each chapter, this book is su
出版日期Book 2017Latest edition
關(guān)鍵詞axiom of choice; Banach-Tarski paradox; cardinal characteristics; combinatorics of forcing; forcing cons
版次2
doihttps://doi.org/10.1007/978-3-319-60231-8
isbn_softcover978-3-319-86812-7
isbn_ebook978-3-319-60231-8Series ISSN 1439-7382 Series E-ISSN 2196-9922
issn_series 1439-7382
copyrightSpringer International Publishing AG 2017
The information of publication is updating

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Models of Set Theory with Atoms another one in which a cardinal . exists such that .. These somewhat strange models are constructed like models of . (see the cumulative hierarchy introduced in Chap.?.). However, instead of starting with the empty set (in order to build the cumulative hierarchy) we start with a set of . and define
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The Shattering Number Revisitedng matrix. However, like other cardinal characteristics, . has different facets. In this chapter we shall see that . is closely related to the ., a combinatorial property of subsets of . (discussed at the end of Chap.?.) which can be regarded as a generalisation of ..
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Coda: A Dual Form of Ramsey’s Theorem by the following fact: Each infinite subset of . corresponds to the . of an . function from . into ., whereas each infinite partition of . corresponds to the set of . of elements of . of a . function from . onto .. Similarly, .-element subsets of . correspond to images of injective functions from .
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The Idea of Forcingto .. In fact, starting from a model of ., Cohen constructed in 1962 models of . in which the . fails as well as models of . in which the . fails. On the other hand, starting from a model of ., G?del constructed a model of . in which the . holds (. Chap.?6). By combining these results we find that t
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