Finite and Infinite Combinatorics in Sets and Logic

This volume contains the accounts of papers delivered at the Nato Advanced Study Institute on Finite and Infinite Combinatorics in Sets and Logic held at the Banff Centre, Alberta, Canada from April 21 to May 4, 1991. As the title suggests the meeting brought together workers interested in the interplay between finite and infinite combinatorics, set theory, graph theory and logic. It used to be that infinite set theory, finite combinatorics and logic could be viewed as quite separate and independent subjects. But more and more those disciplines grow together and become interdependent of each other with ever more problems and results appearing which concern all of those disciplines. I appreciate the financial support which was provided by the N. A. T. O. Advanced Study Institute programme, the Natural Sciences and Engineering Research Council of Canada and the Department of Mathematics and Statistics of the University of Calgary. 11l'te meeting on Finite and Infinite Combinatorics in Sets and Logic followed two other meetings on discrete mathematics held in Banff, the Symposium on Ordered Sets in 1981 and the Symposium on Graphs and Order in 1984. The growing inter-relation between the different areas in discrete mathematics is maybe best illustrated by the fact that many of the participants who were present at the previous meetings also attended this meeting on Finite and Infinite Combinatorics in Sets and Logic.

Klappentext

This book highlights the newly emerging connections between problems in finite combinatorics and graph theory on the one hand and the more foundational subjects of logic and set theory on the other.br/ One of the more obvious routes for such a connection is the straightforward generalization of certain definitions and problems from the finite to the infinite, and sometimes the other way around. Another one is to generalize some definitions and find the appropriate new concepts for the new setting, for example the discussion of ends of graphs.br/ The realization of the importance of homogeneous structures and their connection with logic, as well as with finite structure theory, is a good example of the connection between finite and infinite structures. Almost all of the articles in the present book touch in one way or another on homogeneous structures. The discussion of the 0--1 law, of Ramsey theory for finite and infinite structures, and of divisibility theory highlight this.br/

Inhalt
Extensions of the Erd?sRado Theorem.- Zero Sum Trees: A Survey of Results and Open Problems.- On Superatomic Boolean Algebras.- Representing Rings Using Continuous Function.- Homogeneous Directed Graphs.- Ordinal Partition Behavior of Finite Powers of Cardinals.- Some Subdirect Products of Finite Nilpotent Groups.- Three Remarks on End-Faithfulness.- True Embedding Partition Relations.- Lattices Related to Separation in Graphs.- Ramsey Numbers for Sets of Five Vertex Graphs With Fixed Number of Edges.- Finite Structures With Few Types.- Recognition Problem in Reconstruction for Decomposable Relations.- The Average Size of Nonsingular Sets in a Graph.- Some Canonical Partition Ordinals.- The Group of Automorphisms of a Relational Saturated Structure.- On Canonical Ramsey Numbers for Coloring Three-Element Sets.- Large Subgroups of Infinite Symmetric Groups.- Homogeneous Partially Ordered Sets.- Cardinal Representations.- A Vertex-to-Vertex Pursuit Game Played With Disjoint Sets of Edges.- Graphs and Posets With no Infinite Independent Set.- Problems About Planar Orders.- Superstable and Unstable Theories of Order.- Advances in Cardinal Arithmetic.- Conjectures of Rado and Chang and Cardinal Arithmetic.- Random Structures and Zero-One Laws.- Isotone Maps: Enumeration and Structure.- Problem Sessions.