Ordered Sets [E-Book] : Proceedings of the NATO Advanced Study Institute held at Banff, Canada, August 28 to September 12, 1981 / edited by Ivan Rival.
Rival, Ivan, (editor)
Dordrecht : Springer, 1982
978 p. online resource.
NATO Advanced Study Institutes Series, Series C — Mathematical and Physical Sciences ; 83
Full Text
Table of Contents:
  • I. Structure and Arithmetic of Ordered Sets
  • Arithmetic of ordered sets
  • Exponentiation and duality
  • The retract construction
  • II. Linear Extensions
  • Linear extensions of ordered sets
  • Dimension theory for ordered sets
  • Linear extensions of partial orders and the FKG inequality
  • III. Set Theory and Recursion
  • Order types of real numbers and other uncountable orderings
  • On the cofinality of partially ordered sets
  • Infinite ordered sets, a recursive perspective
  • IV. Lattice Theory
  • The role of order in lattice theory
  • Some order theoretic questions about free lattices and free modular lattices
  • An introduction to the theory of continuous lattices
  • Ordered sets in geometry
  • Restructuring lattice theory: an approach based on hierarchies of concepts
  • V. Enumeration
  • Extremal problems in partially ordered sets
  • Enumeration in classes of ordered structures
  • The Möbius function of a partially ordered set
  • An introduction to Cohen-Macaulay partially ordered sets
  • VI. Applications of Ordered Sets to Computer Sciences
  • Ordered sets and linear programming
  • Machine scheduling with precedence constraints
  • Some ordered sets in computer science
  • VII. Applications of Ordered Sets to Social Sciences
  • Ordered sets and social sciences
  • Some social science applications of ordered sets
  • VIII. Problem Sessions
  • Order types
  • Combinatorics
  • Linear extensions of finite ordered sets
  • Scheduling and sorting
  • Graphs and enumeration
  • Social science and operations research
  • Recursion and game theory
  • Order-preserving maps
  • Lattices
  • Miscellaneous
  • IX. A Bibliography.