Ordered Sets

Ordered Sets
Author: Ivan Rival
Publisher: Springer Science & Business Media
Total Pages: 963
Release: 2012-12-06
Genre: Computers
ISBN: 9400977980
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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.

A Compendium of Continuous Lattices

A Compendium of Continuous Lattices
Author: G. Gierz
Publisher: Springer Science & Business Media
Total Pages: 390
Release: 2012-12-06
Genre: Mathematics
ISBN: 3642676782
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A mathematics book with six authors is perhaps a rare enough occurrence to make a reader ask how such a collaboration came about. We begin, therefore, with a few words on how we were brought to the subject over a ten-year period, during part of which time we did not all know each other. We do not intend to write here the history of continuous lattices but rather to explain our own personal involvement. History in a more proper sense is provided by the bibliography and the notes following the sections of the book, as well as by many remarks in the text. A coherent discussion of the content and motivation of the whole study is reserved for the introduction. In October of 1969 Dana Scott was lead by problems of semantics for computer languages to consider more closely partially ordered structures of function spaces. The idea of using partial orderings to correspond to spaces of partially defined functions and functionals had appeared several times earlier in recursive function theory; however, there had not been very sustained interest in structures of continuous functionals. These were the ones Scott saw that he needed. His first insight was to see that - in more modern terminology - the category of algebraic lattices and the (so-called) Scott-continuous functions is cartesian closed.

Stone Spaces

Stone Spaces
Author: Peter T. Johnstone
Publisher: Cambridge University Press
Total Pages: 398
Release: 1982
Genre: Mathematics
ISBN: 9780521337793
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A unified treatment of the corpus of mathematics that has developed out of M. H. Stone's representation theorem for Boolean algebras (1936) which has applications in almost every area of modern mathematics.

Complexity, Logic, and Recursion Theory

Complexity, Logic, and Recursion Theory
Author: Andrea Sorbi
Publisher: CRC Press
Total Pages: 380
Release: 2019-05-07
Genre: Mathematics
ISBN: 1482269759
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"Integrates two classical approaches to computability. Offers detailed coverage of recent research at the interface of logic, computability theory, nd theoretical computer science. Presents new, never-before-published results and provides informtion not easily accessible in the literature."

Spectral Spaces

Spectral Spaces
Author: Max Dickmann
Publisher: Cambridge University Press
Total Pages: 652
Release: 2019-03-21
Genre: Mathematics
ISBN: 1108609597
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Spectral spaces are a class of topological spaces. They are a tool linking algebraic structures, in a very wide sense, with geometry. They were invented to give a functional representation of Boolean algebras and distributive lattices and subsequently gained great prominence as a consequence of Grothendieck's invention of schemes. There are more than 1,000 research articles about spectral spaces, but this is the first monograph. It provides an introduction to the subject and is a unified treatment of results scattered across the literature, filling in gaps and showing the connections between different results. The book includes new research going beyond the existing literature, answering questions that naturally arise from this comprehensive approach. The authors serve graduates by starting gently with the basics. For experts, they lead them to the frontiers of current research, making this book a valuable reference source.

Ordered Algebraic Structures

Ordered Algebraic Structures
Author: W. B. Powell
Publisher: CRC Press
Total Pages: 220
Release: 1985-10-01
Genre: Mathematics
ISBN: 9780824773427
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The papers contained in this volume constitute the proceedings of the Special Session on Ordered Algebraic Structures which was held at the 1982 annual meeting of the American Mathematical Society in Cincinnati, Ohio. The Special Session and this volume honor Paul Conrad, whose work on the subject is noted for its depth and originality. These papers address many areas within the subject of ordered algebraic structures, including varieties, free algebras, lattice ordered groups, subgroups of ordered groups, semigroups, ordered rings, and topological properties of these structures.