A unified approach to structural limits and limits of graphs with bounded tree-depth /

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...

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Bibliographic Details
Call Number:Libro Electrónico
Main Authors: Nešetřil, Jaroslav (Author), Mendez, Patrice Ossona de (Author)
Format: Electronic eBook
Language:Inglés
Published: Providence, RI : American Mathematical Society, [2020].
Series:Memoirs of the American Mathematical Society ; no. 1272.
Subjects:
Graph theory.
Análisis combinatorio
Teoría de grafos
Lógica matemática
Graph theory
Mathematical logic and foundations > Model theory > Finite structures [See also 68Q15, 68Q19].
Mathematical logic and foundations > Model theory > Applications of model theory [See also 03C60].
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.
Order, lattices, ordered algebraic structures [See also 18B35] > Boolean algebras (Boolean rings) [See also 03G05] > Stone spaces (Boolean spaces) and related structures.
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.
Online Access:Texto completo
Table of 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
  • 4.3. Limits of Graphs with Bounded Tree-depth
  • Chapter 5. Concluding Remarks
  • 5.1. Selected Problems
  • 5.2. Addendum
  • Acknowledgements
  • Bibliography
  • Back Cover

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