Finite and Infinite Combinatorics in Sets and Logic

1. Front Matter

   Pages i-xvii

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2. Extensions of the Erdős—Rado Theorem

   • James E. Baumgartner, András Hajnal, Stevo Todorčević

   Pages 1-17

3. Zero Sum Trees: A Survey of Results and Open Problems

   • A. Bialostocki

   Pages 19-29

4. On Superatomic Boolean algebras

   • Robert Bonnet

   Pages 31-62

5. Representing Rings Using Continuous Functions

   • Andrew B. Carson

   Pages 63-79

6. Homogeneous Directed Graphs

   • Gregory L. Cherlin

   Pages 81-95

7. Ordinal Partition Behavior of Finite Powers of Cardinals

   • Paul Erdős, A. Hajnal, Jean A. Larson

   Pages 97-115

8. Some Subdirect Products of Finite Nilpotent Groups

   • David M. Evans

   Pages 117-124

9. Three Remarks on End-Faithfulness

   • Geňa Hahn, Jozef Širáň

   Pages 125-133

10. True Embedding Partition Relations

    • A. Hajnal

    Pages 135-151

11. Lattices Related to Separation in Graphs

    • R. Halin

    Pages 153-167

12. Ramsey Numbers for Sets of Five Vertex Graphs With Fixed Number of Edges

    • Heiko Harborth

    Pages 169-174

13. Finite Structures with Few Types

    • Ehud Hrushovski

    Pages 175-187

14. Recognition Problem in Reconstruction for Decomposable Relations

    • Pierre Ille

    Pages 189-198

15. The Average Size of Nonsingular Sets in a Graph

    • Wilfried Imrich, Norbert Sauer, Wolfgang Woess

    Pages 199-205

16. Some Canonical Partition Ordinals

    • Jean A. Larson

    Pages 207-224

17. The Group of Automorphisms of a Relational Saturated Structure

    • D. Lascar

    Pages 225-236

18. On Canonical Ramsey Numbers for Coloring Three-Element Sets

    • Hanno Lefmann, Vojtěch Rödl

    Pages 237-247

19. Large Subgroups of Infinite Symmetric Groups

    • Dugald Macpherson

    Pages 249-278

20. Homogeneous Partially Ordered Sets

    • Alan H. Mekler

    Pages 279-288

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.

• Boolean algebra
• Graph
• Graph theory
• Vertex
• cardinals
• logic
• set theory

• Department of Mathematics and Statistics, The University of Calgary, Calgary, Canada

  N. W. Sauer, R. E. Woodrow, B. Sands

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