Nonstandard methods in Ramsey theory and combinatorial number theory /
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| Author / Creator: | Di Nasso, Mauro, 1963- author. |
|---|---|
| Imprint: | Cham, Switzerland : Springer, [2019] |
| Description: | 1 online resource (xvi, 206 pages) : illustrations |
| Language: | English |
| Series: | Lecture notes in mathematics ; 2239 Lecture notes in mathematics (Springer-Verlag) ; 2239. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11895878 |
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| 100 | 1 | |a Di Nasso, Mauro, |d 1963- |e author. |0 http://id.loc.gov/authorities/names/n2005080853 | |
| 245 | 1 | 0 | |a Nonstandard methods in Ramsey theory and combinatorial number theory / |c Mauro Di Nasso, Isaac Goldbring, Martino Lupini. |
| 264 | 1 | |a Cham, Switzerland : |b Springer, |c [2019] | |
| 300 | |a 1 online resource (xvi, 206 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics ; |v 2239 | |
| 504 | |a Includes bibliographical references and index. | ||
| 520 | |a 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. | ||
| 588 | 0 | |a Online resource; title from digital title page (viewed on June 25, 2019). | |
| 505 | 0 | |a Part I Preliminaries. -- Ultrafilters. -- Nonstandard Analysis. -- Hyperfinite Generators of Ultrafilters. -- Many Stars: Iterated Nonstandard Extensions. -- LoebMeasure. -- Part II Ramsey Theory. -- Ramsey's Theorem. -- The Theorems of van der Waerden and Hales-Jewett. -- From Hindman to Gowers. -- Partition Regularity of Equations. -- Part III Combinatorial Number Theory. -- Densities and Structural Properties. -- Working in the Remote Realm. -- Jin's Sumset Theorem. -- Sumset Configurations in Sets of Positive Density. -- Near Arithmetic Progressions in Sparse Sets. -- The Interval Measure Property. -- Part IV Other Topics. -- Triangle Removal and Szemerédi Regularity. -- Approximate Groups. -- Foundations of Nonstandard Analysis. | |
| 650 | 0 | |a Ramsey theory. |0 http://id.loc.gov/authorities/subjects/sh85111302 | |
| 650 | 0 | |a Combinatorial number theory. |0 http://id.loc.gov/authorities/subjects/sh85028808 | |
| 650 | 0 | |a Number theory. |0 http://id.loc.gov/authorities/subjects/sh85093222 | |
| 650 | 7 | |a Combinatorial number theory. |2 fast |0 (OCoLC)fst00868979 | |
| 650 | 7 | |a Number theory. |2 fast |0 (OCoLC)fst01041214 | |
| 650 | 7 | |a Ramsey theory. |2 fast |0 (OCoLC)fst01089712 | |
| 655 | 4 | |a Electronic books. | |
| 700 | 1 | |a Goldbring, Isaac, |e author. | |
| 700 | 1 | |a Lupini, Martino, |e author. |0 http://id.loc.gov/authorities/names/nb2015022953 | |
| 776 | 0 | 8 | |i Print version: |a Di Nasso, Mauro, 1963- |t Nonstandard methods in Ramsey theory and combinatorial number theory. |d Cham, Switzerland : Springer, [2019] |z 3030179559 |z 9783030179557 |w (OCoLC)1090011870 |
| 830 | 0 | |a Lecture notes in mathematics (Springer-Verlag) ; |v 2239. |0 http://id.loc.gov/authorities/names/n42015165 | |
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| 928 | |t Library of Congress classification |a QA166 .D5 2019 |l Online |c UC-FullText |u https://link.springer.com/10.1007/978-3-030-17956-4 |z Springer Nature |g ebooks |i 12561582 | ||