| Document Type
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BL
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| Record Number
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850305
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| Main Entry
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Katz, Matthew,1986-
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| Title & Author
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An introduction to Ramsey theory : : fast functions, infinity, and metamathematics /\ Matthew Katz, Jan Reimann.
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| Publication Statement
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Providence, Rhode Island :: American Mathematical Society,, [2018]
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| Series Statement
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Student mathematical library ;; 87
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| Page. NO
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xiv, 207 pages :: illustrations ;; 22 cm.
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| ISBN
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1470442906
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: 9781470442903
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| Notes
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"Mathematics Advanced Study Semesters."
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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Graph Ramsey theory -- Infinite Ramsey theory -- Growth of Ramsey functions -- Metamathematics.
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| Abstract
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"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, Gödel 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."--
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| Subject
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Combinatorial analysis.
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| Subject
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Ramsey theory.
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| Subject
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Combinatorial analysis.
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| Subject
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Combinatorics -- Extremal combinatorics -- Ramsey theory.
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| Subject
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Mathematical logic and foundations -- Computability and recursion theory -- Recursive functions and relations, subrecursive hierarchies.
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Mathematical logic and foundations -- General logic -- Classical first-order logic.
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| Subject
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Mathematical logic and foundations -- General logic -- Decidability of theories and sets of sentences.
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| Subject
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Mathematical logic and foundations -- Instructional exposition (textbooks, tutorial papers, etc.).
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| Subject
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Mathematical logic and foundations -- Nonstandard models -- Nonstandard models of arithmetic.
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| Subject
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Mathematical logic and foundations -- Set theory -- Ordinal and cardinal numbers.
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| Subject
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Ramsey theory.
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| Dewey Classification
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511/.66
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| LC Classification
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QA165.K38 2018
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| NLM classification
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03H15.msc
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05D1003-0103E1003B1003B2503D2003H15msc
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| Added Entry
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Reimann, Jan,1971-
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| Added Entry
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Pennsylvania State University., Mathematics Advanced Study Semesters.
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