An introduction to Ramsey theory : fast functions, infinity, and metamathematics / Matthew Katz, Jan Reimann

By: Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Student mathematical library ; volume 87Publisher: Providence, Rhode Island : American Mathematical Society, [2018]Description: 1 Online-Ressource (224 p)Subject(s): Additional physical formats: 1470442906 | 9781470442903 | 1470449943 | 9781470449940 | Erscheint auch als: An Introduction to Ramsey Theory : Fast Functions, Infinity, and Metamathematics. Druck-Ausgabe Providence : American Mathematical Society,c2018DDC classification:
  • 511/.66
MSC: MSC: *05D10 | 05C55 | 03E10 | 03D20LOC classification:
  • QA165
Online resources: Summary: 2.7. Large cardinals and Ramsey cardinalsChapter 3. Growth of Ramsey functions; 3.1. Van der Waerden's theorem; 3.2. Growth of van der Waerden bounds; 3.3. Hierarchies of growth; 3.4. The Hales-Jewett theorem; 3.5. A really fast-growing Ramsey function; Chapter 4. Metamathematics; 4.1. Proof and truth; 4.2. Non-standard models of Peano arithmetic; 4.3. Ramsey theory in Peano arithmetic; 4.4. Incompleteness; 4.5. Indiscernibles; 4.6. Diagonal indiscernibles via Ramsey theory; 4.7. The Paris-Harrington theorem; 4.8. More incompleteness; Bibliography; Notation; Index; Back CoverSummary: This book takes the reader on a journey through Ramsey theory, from graph theory and combinatorics to set theory to logic and metamathematics. Written in an informal style with few requisites, it develops two basic principles of Ramsey theory: many combinatorial properties persist under partitions, but to witness this persistence, one has to start with very large objects. The interplay between those two principles not only produces beautiful theorems but also touches the very foundations of mathematics. In the course of this book, the reader will learn about both aspects. Among the topics explPPN: PPN: 1045411515Package identifier: Produktsigel: ZDB-4-NLEBK
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