Cherlin S Conjecture For Finite Primitive Binary Permutation Groups
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Cherlin’s Conjecture for Finite Primitive Binary Permutation Groups
This book gives a proof of Cherlin’s conjecture for finite binary primitive permutation groups. Motivated by the part of model theory concerned with Lachlan’s theory of finite homogeneous relational structures, this conjecture proposes a classification of those finite primitive permutation groups that have relational complexity equal to 2. The first part gives a full introduction to Cherlin’s conjecture, including all the key ideas that have been used in the literature to prove some of its special cases. The second part completes the proof by dealing with primitive permutation groups that are almost simple with socle a group of Lie type. A great deal of material concerning properties of primitive permutation groups and almost simple groups is included, and new ideas are introduced. Addressing a hot topic which cuts across the disciplines of group theory, model theory and logic, this book will be of interest to a wide range of readers. It will be particularly useful for graduate students and researchers who need to work with simple groups of Lie type.
Homogeneous Ordered Graphs, Metrically Homogeneous Graphs, and Beyond
Author: Gregory Cherlin
language: en
Publisher: Cambridge University Press
Release Date: 2022-07-07
The second of two volumes presenting the state of the art in the classification of homogeneous structures and related problems in the intersection of model theory and combinatorics. It extends the results of the first volume to generalizations of graphs and tournaments with additional binary relations. An appendix explores open problems.
Complexity of Infinite-Domain Constraint Satisfaction
Author: Manuel Bodirsky
language: en
Publisher: Cambridge University Press
Release Date: 2021-06-10
Constraint Satisfaction Problems (CSPs) are natural computational problems that appear in many areas of theoretical computer science. Exploring which CSPs are solvable in polynomial time and which are NP-hard reveals a surprising link with central questions in universal algebra. This monograph presents a self-contained introduction to the universal-algebraic approach to complexity classification, treating both finite and infinite-domain CSPs. It includes the required background from logic and combinatorics, particularly model theory and Ramsey theory, and explains the recently discovered link between Ramsey theory and topological dynamics and its implications for CSPs. The book will be of interest to graduate students and researchers in theoretical computer science and to mathematicians in logic, combinatorics, and dynamics who wish to learn about the applications of their work in complexity theory.