Overview

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.

Full Product Details

Author:   Ivan Rival
Publisher:   Springer
Imprint:   Springer
Edition:   Softcover reprint of the original 1st ed. 1982
Volume:   83
Dimensions:   Width: 15.50cm , Height: 4.90cm , Length: 23.50cm
Weight:   1.484kg
ISBN:  

9789400978003

ISBN 10:   9400978006
Pages:   978
Publication Date:   03 November 2011
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

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.

Reviews

Author Information

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions