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000890858 019__ $$a1103473535
000890858 020__ $$a9783030179564$$q(electronic book)
000890858 020__ $$a3030179567$$q(electronic book)
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000890858 0247_ $$a10.1007/978-3-030-17$$2doi
000890858 035__ $$aSP(OCoLC)on1105176833
000890858 035__ $$aSP(OCoLC)1105176833$$z(OCoLC)1103473535
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000890858 050_4 $$aQA166$$b.D5 2019
000890858 08204 $$a511.6$$223
000890858 1001_ $$aDi Nasso, Mauro,$$d1963-$$eauthor.
000890858 24510 $$aNonstandard methods in Ramsey theory and combinatorial number theory /$$cMauro Di Nasso, Isaac Goldbring, Martino Lupini.
000890858 264_1 $$aCham, Switzerland :$$bSpringer,$$c[2019]
000890858 300__ $$a1 online resource (xvi, 206 pages) :$$billustrations.
000890858 336__ $$atext$$btxt$$2rdacontent
000890858 337__ $$acomputer$$bc$$2rdamedia
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000890858 4901_ $$aLecture notes in mathematics ;$$v2239
000890858 504__ $$aIncludes bibliographical references and index.
000890858 5050_ $$aPart 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.
000890858 506__ $$aAccess limited to authorized users.
000890858 520__ $$aThe 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.
000890858 588__ $$aDescription based on online resource; title from digital title page (viewed on June 25, 2019).
000890858 650_0 $$aRamsey theory.
000890858 650_0 $$aCombinatorial number theory.
000890858 650_0 $$aNumber theory.
000890858 7001_ $$aGoldbring, Isaac,$$eauthor.
000890858 7001_ $$aLupini, Martino,$$eauthor.
000890858 77608 $$iPrint version$$z3030179559$$z9783030179557$$w(OCoLC)1090011870
000890858 830_0 $$aLecture notes in mathematics (Springer-Verlag) ;$$v2239.
000890858 85280 $$bebk$$hSpringerLink
000890858 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-030-17956-4$$zOnline Access$$91397441.1
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