An Introduction to Ramsey Theory: Fast Functions, Infinity, and Metamathematics - Couverture souple

Katz, Matthew; Reimann, Jan

Couverture souple

ISBN 10 : 1470442906 ISBN 13 : 9781470442903

Editeur : American Mathematical Society, 2018

Synopsis

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 explored are Ramsey's theorem for graphs and hypergraphs, van der Waerden's theorem on arithmetic progressions, infinite ordinals and cardinals, fast growing functions, logic and provability, Godel incompleteness, and the Paris-Harrington theorem.

Quoting from the book, ``There seems to be a murky abyss lurking at the bottom of mathematics. While in many ways we cannot hope to reach solid ground, mathematicians have built impressive ladders that let us explore the depths of this abyss and marvel at the limits and at the power of mathematical reasoning at the same time. Ramsey theory is one of those ladders.'' This book is published in cooperation with Mathematics Advanced Study Semesters.

A propos du livre

À propos de l'auteur

Matthew Katz, Pennsylvania State University, University Park, PA.

Jan Reimann, Pennsylvania State University, University Park, PA.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2018
• Langue: anglais
• ISBN 10: 1470442906
• ISBN 13: 9781470442903
• Reliure: Broché
• Nombre de pages: 207
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible