| Description |
1 online resource (v, 108 pages) |
| Series |
Memoirs of the American Mathematical Society, 0065-9266 ; number 1272 |
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Memoirs of the American Mathematical Society ; no. 1272. 0065-9266
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| Contents |
Cover -- Title page -- Chapter 1. Introduction -- 1.1. Main Definitions and Results -- Chapter 2. General Theory -- 2.1. Limits as Measures on Stone Spaces -- 2.2. Convergence, Old and New -- 2.3. Combining Fragments -- 2.4. Interpretation Schemes -- Chapter 3. Modelings for Sparse Structures -- 3.1. Relational Samples Spaces -- 3.2. Modelings -- 3.3. Decomposing Sequences: the Comb Structure -- Chapter 4. Limits of Graphs with Bounded Tree-depth -- 4.1. ₁-limits of Colored Rooted Trees with Bounded Height -- 4.2.-limits of Colored Rooted Trees with Bounded Height |
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4.3. Limits of Graphs with Bounded Tree-depth -- Chapter 5. Concluding Remarks -- 5.1. Selected Problems -- 5.2. Addendum -- Acknowledgements -- Bibliography -- Back Cover |
| Summary |
In this paper the authors introduce a general framework for the study of limits of relational structures and graphs in particular, which is based on a combination of model theory and (functional) analysis. The authors show how the various approaches to graph limits fit to this framework and that the authors naturally appear as ""tractable cases"" of a general theory. As an outcome of this, the authors provide extensions of known results. The authors believe that this puts these into a broader context. The second part of the paper is devoted to the study of sparse structures. First, the authors |
| Bibliography |
Includes bibliographical references |
| Notes |
Online resource, title from digital title page (viewed on March 24, 2021) |
| Subject |
Graph theory.
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Análisis combinatorio
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Teoría de grafos
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Lógica matemática
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Graph theory
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Mathematical logic and foundations -- Model theory -- Finite structures [See also 68Q15, 68Q19].
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Mathematical logic and foundations -- Model theory -- Applications of model theory [See also 03C60].
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Combinatorics {For finite fields, see 11Txx} -- Graph theory {For applications of graphs, see 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15} -- None of the above, but in this section.
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Order, lattices, ordered algebraic structures [See also 18B35] -- Boolean algebras (Boolean rings) [See also 03G05] -- Stone spaces (Boolean spaces) and related structures.
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Measure and integration {For analysis on manifolds, see 58-XX} -- Set functions and measures on spaces with additional structure [See also 46G12, 58C35, 58D20] -- Integration theory via linear functio.
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| Form |
Electronic book
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| Author |
Mendez, Patrice Ossona de, author
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| ISBN |
9781470456528 |
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1470456524 |
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