Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory
| Autor: | Martino Lupini, Mauro Di Nasso, Isaac Goldbring |
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| Rok vydání: | 2019 |
| Předmět: |
Discrete mathematics
Mathematics::Combinatorics Ramsey theory Mathematics::General Topology Sumset Ramsey Theory Nonstandard Analysis Measure (mathematics) Combinatorics Mathematics::Logic Iterated function Barycentric-sum problem Partition regularity Van der Waerden's theorem Interval (graph theory) Combinatorics Nonstandard Analysis Ramsey Theory Mathematics |
| Zdroj: | Lecture Notes in Mathematics ISBN: 9783030179557 Lecture Notes in Mathematics |
| DOI: | 10.1007/978-3-030-17956-4 |
| Popis: | 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 Szemeredi Regularity. - Approximate Groups. - Foundations of Nonstandard Analysis. |
| Databáze: | OpenAIRE |
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