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An Introduction to Ramsey Theory: Fast Functions, Infinity, and Metamathematics (Student Mathematical Library) - Tapa blanda

Katz, Matthew; Reimann, Jan

 
9781470442903: An Introduction to Ramsey Theory: Fast Functions, Infinity, and Metamathematics (Student Mathematical Library)
Tapa blanda
ISBN 10: 1470442906 ISBN 13: 9781470442903
Editorial: American Mathematical Society, 2018

Sinopsis

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.

"Sinopsis" puede pertenecer a otra edición de este libro.

Acerca del autor

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

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

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
American Mathematical Society
Año de publicación
2018
Idioma
Inglés
ISBN 10 
1470442906
ISBN 13 
9781470442903
Encuadernación
Tapa blanda
Número de páginas
207
Contacto del fabricante
no disponible
Persona responsable
no disponible