Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory [electronic resource] / by Mauro Di Nasso, Isaac Goldbring, Martino Lupini.
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TextSeries: Lecture Notes in Mathematics ; 2239Publisher: Cham : Springer International Publishing : Imprint: Springer, 2019Edition: 1st ed. 2019Description: XVI, 206 p. 2 illus. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783030179564Subject(s): Combinatorics | Mathematical logic | Combinatorics | Mathematical Logic and FoundationsAdditional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification: 511.6 LOC classification: QA164-167.2Online resources: Click here to access online
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Springer eBooksSummary: 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.
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.