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Ordered Sets

Proceedings of the NATO Advanced Study Institute held at Banff, Canada, August 28 to September 12, 1981

  • Ivan Rival

Part of the NATO Advanced Study Institutes Series book series (ASIC, volume 83)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Structure and Arithmetic of Ordered Sets

    1. Front Matter
      Pages 1-1
    2. Bjarni Jónsson
      Pages 3-41
    3. B. A. Davey, D. Duffus
      Pages 43-95
    4. Ivan Rival
      Pages 97-122
  3. Linear Extensions

    1. Front Matter
      Pages 123-123
    2. R. Bonnet, M. Pouzet
      Pages 125-170
    3. David Kelly, William T. Trotter Jr.
      Pages 171-211
  4. Set Theory and Recursion

    1. Front Matter
      Pages 237-237
    2. E. C. Milner, M. Pouzet
      Pages 279-298
    3. George F. McNulty
      Pages 299-330
  5. Lattice Theory

    1. Front Matter
      Pages 331-331
    2. R. P. Dilworth
      Pages 333-353
    3. Ivan Rival
      Pages 376-377
    4. Michael W. Mislove
      Pages 379-406
    5. Garrett Birkhoff
      Pages 407-443
  6. Enumeration

    1. Front Matter
      Pages 471-471
    2. Douglas B. West
      Pages 473-521
    3. Robert W. Quackenbush
      Pages 523-554
    4. A. Björner, A. M. Garsia, R. P. Stanley
      Pages 583-615
  7. Applications of Ordered Sets to Computer Sciences

    1. Front Matter
      Pages 617-617
    2. A. J. Hoffman
      Pages 619-654
    3. E. L. Lawler, J. K. Lenstra
      Pages 655-675
    4. Dana S. Scott
      Pages 677-718
  8. Applications of Ordered Sets to Social Sciences

    1. Front Matter
      Pages 719-719
    2. J. P. Barthélemy, Cl. Flament, B. Monjardet
      Pages 721-758
    3. Ivan Rival
      Pages 758-758
  9. Problem Sessions

    1. Front Matter
      Pages 789-792
    2. Ivan Rival
      Pages 793-798
    3. Ivan Rival
      Pages 799-805
    4. Ivan Rival
      Pages 806-811
    5. Ivan Rival
      Pages 812-817
    6. Ivan Rival
      Pages 818-823
    7. Ivan Rival
      Pages 824-828
    8. Ivan Rival
      Pages 829-835
    9. Ivan Rival
      Pages 836-843
    10. Ivan Rival
      Pages 844-850
    11. Ivan Rival
      Pages 851-861
  10. Back Matter
    Pages 863-966

About these proceedings

Introduction

This volume contains all twenty-three of the principal survey papers presented at the Symposium on Ordered Sets held at Banff, Canada from August 28 to September 12, 1981. The Symposium was supported by grants from the NATO Advanced Study Institute programme, the Natural Sciences and Engineering Research Council of Canada, the Canadian Mathematical Society Summer Research Institute programme, and the University of Calgary. tve are very grateful to these Organizations for their considerable interest and support. Over forty years ago on April 15, 1938 the first Symposium on Lattice Theory was held in Charlottesville, U.S.A. in conjunction with a meeting of the American Mathematical Society. The principal addresses on that occasion were Lattices and their applications by G. Birkhoff, On the application of structure theory to groups by O. Ore, and The representation of Boolean algebras by M. H. Stone. The texts of these addresses and three others by R. Baer, H. M. MacNeille, and K. Menger appear in the Bulletin of the American Mathematical Society, Volume 44, 1938. In those days the theory of ordered sets, and especially lattice theory was described as a "vigorous and promising younger brother of group theory." Some early workers hoped that lattice­ theoretic methods would lead to solutions of important problems in group theory.

Keywords

Lattice combinatorics computer computer science game theory geometry programming sets

Editors and affiliations

  • Ivan Rival
    • 1
  1. 1.Department of Mathematics and StatisticsThe University of CalgaryCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-009-7798-3
  • Copyright Information Springer Science+Business Media B.V. 1982
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-009-7800-3
  • Online ISBN 978-94-009-7798-3
  • Series Print ISSN 1389-2185
  • Buy this book on publisher's site
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