Introduction to Ramsey Spaces

Ramsey theory is a fast-growing area of combinatorics with deep connections to other fields of mathematics such as topological dynamics, ergodic theory, mathematical logic, and algebra. The area of Ramsey theory dealing with Ramsey-type phenomena in higher dimensions is particularly useful. Introduc...

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Bibliographische Detailangaben
1. Verfasser:	Todorcevic, Stevo
Format:	E-Book Buch
Sprache:	Englisch
Veröffentlicht:	Princeton Princeton University Press 2010
Ausgabe:	1
Schriftenreihe:	Annals of mathematics studies
Schlagworte:	Algebraic spaces Analytic set Axiom of choice Baire category theorem Baire space Banach space Bijection Binary relation Boolean prime ideal theorem Borel equivalence relation Borel measure Borel set Cantor cube Cantor set Cantor space Characterization (mathematics) Combinatorics Compactification (mathematics) Complete metric space Constructible universe Continuous function Continuous function (set theory) Corollary Diagonalization Dimension Dimension (vector space) Disjoint sets Equation Equivalence relation Family of sets Forcing (mathematics) Forcing (recursion theory) Gap theorem Ideal (ring theory) Infinite product Lebesgue measure Limit point Lipschitz continuity Mathematical induction MATHEMATICS MATHEMATICS / Combinatorics MATHEMATICS / General Metric space Metrization theorem Monotonic function Natural number Natural topology Open set Order type Peano axioms Polish space Probability measure Product measure Product topology Property of Baire Ramsey theory Ramsey's theorem Right inverse Scalar multiplication Schauder basis Semigroup Sequential space Set (mathematics) Set theory Subsequence Subset Subspace topology Theorem Topological group Topological space Topology Variable (mathematics) Zorn's lemma Equivalence relation Open set Bijection Subset Forcing (recursion theory) Limit point Product measure Ramsey theory Forcing (mathematics) Cantor set Borel equivalence relation Mathematical induction Characterization (mathematics) Infinite product Order type Combinatorics Corollary Monotonic function Ideal (ring theory) Right inverse Baire category theorem Semigroup Continuous function Natural topology Topology Sequential space Subspace topology Binary relation Dimension (vector space) Zorn's lemma Topological space Gap theorem Subsequence Boolean prime ideal theorem Disjoint sets Axiom of choice Probability measure Natural number Complete metric space Continuous function (set theory) Diagonalization Metric space Product topology Ramsey's theorem Set (mathematics) C0 Cantor space Lipschitz continuity Family of sets Lebesgue measure Baire space Theorem Polish space Metrization theorem Borel measure Peano axioms Constructible universe Cantor cube Borel set Equation Dimension Banach space Analytic set Property of Baire Variable (mathematics) Topological group Compactification (mathematics) Set theory Schauder basis Scalar multiplication
ISBN:	0691145415, 9780691145419, 9780691145426, 0691145423, 1400835402, 9781400835409
Online-Zugang:	Volltext
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Inhaltsangabe:

Introduction to Ramsey Spaces -- Contents -- Introduction -- Chapter One: Ramsey Theory: Preliminaries -- Chapter Two: Semigroup Colorings -- Chapter Three: Trees and Products -- Chapter Four: Abstract Ramsey Theory -- Chapter Five: Topological Ramsey Theory -- Chapter Six: Spaces of Trees -- Chapter Seven: Local Ramsey Theory -- Chapter Eight: Infinite Products of Finite Sets -- Chapter Nine: Parametrized Ramsey Theory -- Appendix -- Bibliography -- Subject Index -- Index of Notation
Front Matter Table of Contents Introduction Chapter One: Ramsey Theory: Chapter Two: Semigroup Colorings Chapter Three: Trees and Products Chapter Four: Abstract Ramsey Theory Chapter Five: Topological Ramsey Theory Chapter Six: Spaces of Trees Chapter Seven: Local Ramsey Theory Chapter Eight: Infinite Products of Finite Sets Chapter Nine: Parametrized Ramsey Theory Appendix Bibliography Subject Index Index of Notation
Cover -- Title -- Copyright -- Contents -- Introduction -- Chapter 1. Ramsey Theory: Preliminaries -- 1.1 Coideals -- 1.2 Dimensions in Ramsey Theory -- 1.3 Higher Dimensions in Ramsey Theory -- 1.4 Ramsey Property and Baire Property -- Chapter 2. Semigroup Colorings -- 2.1 Idempotents in Compact semigroups -- 2.2 The Galvin-Glazer Theorem -- 2.3 Gowers's Theorem -- 2.4 A Semigroup of Subsymmetric Ultrafilters -- 2.5 The Hales-Jewett Theorem -- 2.6 Partial Semigroup of Located Words -- Chapter 3. Trees and Products -- 3.1 Versions of the Halpern-Läuchli Theorem -- 3.2 A Proof of the Halpern-Läuchli Theorem -- 3.3 Products of Finite Sets -- Chapter 4. Abstract Ramsey Theory -- 4.1 Abstract Baire Property -- 4.2 The Abstract Ramsey Theorem -- 4.3 Combinatorial Forcing -- 4.4 The Hales-Jewett Space -- 4.5 Ramsey Spaces of Infinite Block Sequences of Located Words -- Chapter 5. Topological Ramsey Theory -- 5.1 Topological Ramsey Spaces -- 5.2 Topological Ramsey Spaces of Infinite Block Sequences of Vectors -- 5.3 Topological Ramsey Spaces of Infinite Sequences of Variable Words -- 5.4 Parametrized Versions of Rosenthal Dichotomies -- 5.5 Ramsey Theory of Superperfect Subsets of Polish Spaces -- 5.6 Dual Ramsey Theory -- 5.7 A Ramsey Space of Infinite-Dimensional Vector Subspaces of F[sup(N)] -- Chapter 6. Spaces of Trees -- 6.1 A Ramsey Space of Strong Subtrees -- 6.2 Applications of the Ramsey Space of Strong Subtrees -- 6.3 Partition Calculus on Finite Powers of the Countable Dense Linear Ordering -- 6.4 A Ramsey Space of Increasing Sequences of Rationals -- 6.5 Continuous Colorings on Q[sup([k])] -- 6.6 Some Perfect Set Theorems -- 6.7 Analytic Ideals and Points in Compact Sets of the First Baire Class -- Chapter 7. Local Ramsey Theory -- 7.1 Local Ellentuck Theory -- 7.2 Topological Ultra-Ramsey Spaces
7.3 Some Examples of Selective Coideals on N -- 7.4 Some Applications of Ultra-Ramsey Theory -- 7.5 Local Ramsey Theory and Analytic Topologies on N -- 7.6 Ultra-Hales-Jewett Spaces -- 7.7 Ultra-Ramsey Spaces of Block Sequences of Located Words -- 7.8 Ultra-Ramsey Space of Infinite Block Sequences of Vectors -- Chapter 8. Infinite Products of Finite Sets -- 8.1 Semicontinuous Colorings of Infinite Products of Finite Sets -- 8.2 Polarized Ramsey Property -- 8.3 Polarized Partition Calculus -- Chapter 9. Parametrized Ramsey Theory -- 9.1 Higher Dimensional Ramsey Theorems Parametrized by Infinite Products of Finite Sets -- 9.2 Combinatorial Forcing Parametrized by Infinite Products of Finite Sets -- 9.3 Parametrized Ramsey Property -- 9.4 Infinite-Dimensional Ramsey Theorem Parametrized by Infinite Products of Finite Sets -- Appendix -- Bibliography -- Subject Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Z -- Index of Notation
Chapter 4. Abstract Ramsey Theory
Index of Notation
Subject Index
Chapter 3. Trees and Products
Chapter 2. Semigroup Colorings
Chapter 9. Parametrized Ramsey Theory
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Appendix
Chapter 8. Infinite Products of Finite Sets
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Chapter 7. Local Ramsey Theory
Contents
Chapter 6. Spaces of Trees
Chapter 5. Topological Ramsey Theory
Introduction
Frontmatter --
Chapter 1. Ramsey Theory: Preliminaries
Bibliography