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Ordered Sets

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

  • Conference proceedings
  • © 1982

Overview

Editors:
  1. Ivan Rival

    1. Department of Mathematics and Statistics, The University of Calgary, Canada

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Part of the book series: Nato Science Series C: (ASIC, volume 83)

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Table of contents (35 papers)

  1. Front Matter

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

    1. Front Matter

      Pages 1-1
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    2. Arithmetic of Ordered Sets

      • Bjarni Jónsson
      Pages 3-41

    3. Exponentiation and Duality

      • B. A. Davey, D. Duffus
      Pages 43-95

    4. The Retract Construction

      • Ivan Rival
      Pages 97-122

  3. Linear Extensions

    1. Front Matter

      Pages 123-123
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    2. Linear Extensions of Ordered Sets

      • R. Bonnet, M. Pouzet
      Pages 125-170

    3. Dimension Theory for Ordered Sets

      • David Kelly, William T. Trotter Jr.
      Pages 171-211

    4. Linear Extensions of Partial Orders and the FKG Inequality

      • R. L. Graham
      Pages 213-236

  4. Set Theory and Recursion

    1. Front Matter

      Pages 237-237
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    2. Order Types of Real Numbers and Other Uncountable Orderings

      • James E. Baumgartner
      Pages 239-277

    3. On the Cofinality of Partially Ordered Sets

      • E. C. Milner, M. Pouzet
      Pages 279-298

    4. Infinite Ordered Sets, A Recursive Perspective

      • George F. McNulty
      Pages 299-330

  5. Lattice Theory

    1. Front Matter

      Pages 331-331
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    2. The Role of Order in Lattice Theory

      • R. P. Dilworth
      Pages 333-353

    3. Some Order Theoretic Questions About Free Lattices and Free Modular Lattices

      • Ralph Freese
      Pages 355-376

    4. Addendum

      • Ivan Rival
      Pages 376-377

    5. An Introduction to the Theory of Continuous Lattices

      • Michael W. Mislove
      Pages 379-406

    6. Ordered Sets in Geometry

      • Garrett Birkhoff
      Pages 407-443

    7. Restructuring Lattice Theory: An Approach Based on Hierarchies of Concepts

      • Rudolf Wille
      Pages 445-470
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Keywords

About this book

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.

Editors and Affiliations

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

    Ivan Rival

Bibliographic Information

  • Book Title: Ordered Sets

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

  • Editors: Ivan Rival

  • Series Title: Nato Science Series C:

  • DOI: https://doi.org/10.1007/978-94-009-7798-3

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: D. Reidel Publishing Company, Dordrecht, Holland 1982

  • Hardcover ISBN: 978-90-277-1396-4Published: 31 March 1982

  • Softcover ISBN: 978-94-009-7800-3Published: 03 November 2011

  • eBook ISBN: 978-94-009-7798-3Published: 06 December 2012

  • Series ISSN: 1389-2185

  • Edition Number: 1

  • Number of Pages: 978

  • Topics: Discrete Mathematics in Computer Science, Order, Lattices, Ordered Algebraic Structures

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