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.
Table of ContentsPreface. Extensions of the Erdös--Rado Theorem; J.E. Baumgartner, A. Hajnal, S. Todorcevic. Zero Sum Trees: a Survey of Results and Open Problems; A. Bialostocki. On Superatomic Boolean Algebras; R. Bonnet. Representing Rings using Continuous Functions; A.B. Carson. Homogeneous Directed Graphs; G.L. Cherlin. Ordinal Partition Behavior of Finite Powers of Cardinals; P. Erdoös, A. Hajnal, J.A.A. Larson. Some Subdirect Products of Finite Nilpotent Groups; D.M. Evans. Three Remarks on End-Faithfulness; G. Hahn, J. Sirán. True Embedding Partition Relations; A. Hajnal. Lattices related to Separation in Graphs; R. Halin. Ramsey Numbers for Sets of Five Vertex Graphs with Fixed Number of Edges; H. Harborth. Finite Structures with Few Types; E. Hrushovski. Recognition Problem in Reconstruction for Decomposable Relations; P. Ille. The Average Size of Nonsingular Sets in a Graph; W. Imrich, N. Sauer, W. Woess. Some Canonical Partition Ordinals; J.A. Larson. The Group of Automorphisms of a Relational Saturated Structure; D. Lascar. On Canonical Ramsey Numbers for Coloring Three-Element Sets; H. Lefmann, V. Rödl. Large Subgroups of Infinite Symmetric Groups; D. Macpherson. Homogeneous Partially Ordered Sets; A.H. Mekler. Cardinal Representations; E.C. Milner. A Vertex-to-Vertex Pursuit Game played with Disjoint Sets of Edges; S. Neufeld, R.J. Nowakowski. Graphs and Posets with no Infinite Independent Set; M. Pouzet. Problems about Planar Orders; I. Rival. Superstable and Unstable Theories of Order; T.J. Schneider. Advances in Cardinal Arithmetic; S. Shelah. Conjectures of Rado and Chang and Cardinal Arithmetic; S.Todorčević. Random Structures and Zero--One Laws; P. Winkler. Isotone Maps: Enumeration and Structure; N. Zaguia. Problem Sessions.