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Titlebook: Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory; Mauro Di Nasso,Isaac Goldbring,Martino Lupini Book 2019 Springer Nat

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發(fā)表于 2025-3-21 20:10:01 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書(shū)目名稱Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory
編輯Mauro Di Nasso,Isaac Goldbring,Martino Lupini
視頻videohttp://file.papertrans.cn/668/667903/667903.mp4
概述Presents the first introduction to nonstandard methods geared towards combinatorics.Includes new nonstandard proofs of classical results in Ramsey theory.Provides a self-contained introduction to the
叢書(shū)名稱Lecture Notes in Mathematics
圖書(shū)封面Titlebook: Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory;  Mauro Di Nasso,Isaac Goldbring,Martino Lupini Book 2019 Springer Nat
描述.The goal of this monograph is to give an accessible introduction to nonstandard methods and their applications, with an emphasis on combinatorics and Ramsey theory. It includes both new nonstandard proofs of classical results and recent developments initially obtained in the nonstandard setting. This makes it the first combinatorics-focused account of nonstandard methods to be aimed at a general (graduate-level) mathematical audience. This book will provide a natural starting point for researchers interested in approaching the rapidly growing literature on combinatorial results obtained via nonstandard methods. The primary audience consists of graduate students and specialists in logic and combinatorics who wish to pursue research at the interface between these areas..
出版日期Book 2019
關(guān)鍵詞Combinatorial number theory; Nonstandard analysis; Partition regular; Ramsey theory; Ultrafilter; combina
版次1
doihttps://doi.org/10.1007/978-3-030-17956-4
isbn_softcover978-3-030-17955-7
isbn_ebook978-3-030-17956-4Series ISSN 0075-8434 Series E-ISSN 1617-9692
issn_series 0075-8434
copyrightSpringer Nature Switzerland AG 2019
The information of publication is updating

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Lecture Notes in Mathematicshttp://image.papertrans.cn/n/image/667903.jpg
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Mauro Di Nasso,Isaac Goldbring,Martino LupiniPresents the first introduction to nonstandard methods geared towards combinatorics.Includes new nonstandard proofs of classical results in Ramsey theory.Provides a self-contained introduction to the
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Densities and Structural Propertiess of any finite partition of a given structure. Such a notion can be strengthened by considering combinatorial configuration that can be found in any set that is “l(fā)arge” in a more generous quantitative sense.
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Jin’s Sumset Theorem methods. We present Jin’s original nonstandard proof, as well as an ultrafilter proof due to Beiglb?ck and an alternative nonstandard proof due to Di Nasso. In the final section, we prove a recent quantitative strengthening of Jin’s Sumset Theorem.
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