Reverse Mathematics On Lattice Ordered Groups
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Theory Of Lattice Ordered Groups
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Author : Michael Darnel
language : en
Publisher: CRC Press
Release Date : 2021-12-16
Theory Of Lattice Ordered Groups written by Michael Darnel and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-16 with Mathematics categories.
Provides a thorough discussion of the orderability of a group. The book details the major developments in the theory of lattice-ordered groups, delineating standard approaches to structural and permutation representations. A radically new presentation of the theory of varieties of lattice-ordered groups is offered.;This work is intended for pure and applied mathematicians and algebraists interested in topics such as group, order, number and lattice theory, universal algebra, and representation theory; and upper-level undergraduate and graduate students in these disciplines.;College or university bookstores may order five or more copies at a special student price which is available from Marcel Dekker Inc, upon request.
Partially Ordered Groups
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Author : A M W Glass
language : en
Publisher: World Scientific
Release Date : 1999-07-22
Partially Ordered Groups written by A M W Glass and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-07-22 with Mathematics categories.
Recently the theory of partially ordered groups has been used by analysts, algebraists, topologists and model theorists. This book presents the most important results and topics in the theory with proofs that rely on (and interplay with) other areas of mathematics. It concludes with a list of some unsolved problems for the reader to tackle. In stressing both the special techniques of the discipline and the overlap with other areas of pure mathematics, the book should be of interest to a wide audience in diverse areas of mathematics. Contents:Definitions and ExamplesBasic PropertiesValues, Primes and PolarsAbelian and Normal-Valued Lattice-Ordered GroupsArchimedean Function GroupsSoluble Right Partially Ordered Groups and GeneralisationsPermutationsApplicationsCompletionsVarieties of Lattice-Ordered GroupsUnsolved Problems Readership: Pure mathematicians. Keywords:Partially Ordered Group;Lattice Ordered Group;Abelian Lattice Ordered Group;Completion;VarietyReviews: “The author's style of writing is very lucid, and the material presented is self-contained. It is an excellent reference text for a graduate course in this area, as well as a source of material for individual reading.” Bulletin of London Mathematical Society “This monograph is clearly written, well organized … can be warmly recommended to students and research workers dealing with the theory of partially ordered groups.” Mathematics Abstracts “Glass's book will get the reader to the forefront of research in the field and would be a suitable text for students in modern algebra, group theory, or ordered structures. It will surely find its place in all mathematical libraries and on the desks of the professional algebraists and 'ordered-groupers'.” Mathematical Reviews
Lattice Ordered Groups
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Author : M.E Anderson
language : en
Publisher: Springer
Release Date : 2011-10-19
Lattice Ordered Groups written by M.E Anderson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-19 with Computers categories.
The study of groups equipped with a compatible lattice order ("lattice-ordered groups" or "I!-groups") has arisen in a number of different contexts. Examples of this include the study of ideals and divisibility, dating back to the work of Dedekind and continued by Krull; the pioneering work of Hahn on totally ordered abelian groups; and the work of Kantorovich and other analysts on partially ordered function spaces. After the Second World War, the theory of lattice-ordered groups became a subject of study in its own right, following the publication of fundamental papers by Birkhoff, Nakano and Lorenzen. The theory blossomed under the leadership of Paul Conrad, whose important papers in the 1960s provided the tools for describing the structure for many classes of I!-groups in terms of their convex I!-subgroups. A particularly significant success of this approach was the generalization of Hahn's embedding theorem to the case of abelian lattice-ordered groups, work done with his students John Harvey and Charles Holland. The results of this period are summarized in Conrad's "blue notes" [C].
Reverse Mathematics And Ordered Groups
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Author : David Reed Solomon
language : en
Publisher:
Release Date : 1998
Reverse Mathematics And Ordered Groups written by David Reed Solomon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
Ordered Permutation Groups
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Author : Andrew Martin William Glass
language : en
Publisher: Cambridge University Press
Release Date : 1981
Ordered Permutation Groups written by Andrew Martin William Glass and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.
As a result of the work of the nineteenth-century mathematician Arthur Cayley, algebraists and geometers have extensively studied permutation of sets. In the special case that the underlying set is linearly ordered, there is a natural subgroup to study, namely the set of permutations that preserves that order. In some senses. these are universal for automorphisms of models of theories. The purpose of this book is to make a thorough, comprehensive examination of these groups of permutations. After providing the initial background Professor Glass develops the general structure theory, emphasizing throughout the geometric and intuitive aspects of the subject. He includes many applications to infinite simple groups, ordered permutation groups and lattice-ordered groups. The streamlined approach will enable the beginning graduate student to reach the frontiers of the subject smoothly and quickly. Indeed much of the material included has never been available in book form before, so this account should also be useful as a reference work for professionals.
Finitely Supported Mathematics
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Author : Andrei Alexandru
language : en
Publisher: Springer
Release Date : 2016-08-01
Finitely Supported Mathematics written by Andrei Alexandru and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-01 with Computers categories.
In this book the authors present an alternative set theory dealing with a more relaxed notion of infiniteness, called finitely supported mathematics (FSM). It has strong connections to the Fraenkel-Mostowski (FM) permutative model of Zermelo-Fraenkel (ZF) set theory with atoms and to the theory of (generalized) nominal sets. More exactly, FSM is ZF mathematics rephrased in terms of finitely supported structures, where the set of atoms is infinite (not necessarily countable as for nominal sets). In FSM, 'sets' are replaced either by `invariant sets' (sets endowed with some group actions satisfying a finite support requirement) or by `finitely supported sets' (finitely supported elements in the powerset of an invariant set). It is a theory of `invariant algebraic structures' in which infinite algebraic structures are characterized by using their finite supports. After explaining the motivation for using invariant sets in the experimental sciences as well as the connections with the nominal approach, admissible sets and Gandy machines (Chapter 1), the authors present in Chapter 2 the basics of invariant sets and show that the principles of constructing FSM have historical roots both in the definition of Tarski `logical notions' and in the Erlangen Program of Klein for the classification of various geometries according to invariants under suitable groups of transformations. Furthermore, the consistency of various choice principles is analyzed in FSM. Chapter 3 examines whether it is possible to obtain valid results by replacing the notion of infinite sets with the notion of invariant sets in the classical ZF results. The authors present techniques for reformulating ZF properties of algebraic structures in FSM. In Chapter 4 they generalize FM set theory by providing a new set of axioms inspired by the theory of amorphous sets, and so defining the extended Fraenkel-Mostowski (EFM) set theory. In Chapter 5 they define FSM semantics for certain process calculi (e.g., fusion calculus), and emphasize the links to the nominal techniques used in computer science. They demonstrate a complete equivalence between the new FSM semantics (defined by using binding operators instead of side conditions for presenting the transition rules) and the known semantics of these process calculi. The book is useful for researchers and graduate students in computer science and mathematics, particularly those engaged with logic and set theory.
Lattice Ordered Groups
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Author : Paul F. Conrad
language : en
Publisher:
Release Date : 1970
Lattice Ordered Groups written by Paul F. Conrad and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Lattice theory categories.
Ordered Groups And Infinite Permutation Groups
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Author : W.C. Holland
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Ordered Groups And Infinite Permutation Groups written by W.C. Holland and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
The subjects of ordered groups and of infinite permutation groups have long en joyed a symbiotic relationship. Although the two subjects come from very different sources, they have in certain ways come together, and each has derived considerable benefit from the other. My own personal contact with this interaction began in 1961. I had done Ph. D. work on sequence convergence in totally ordered groups under the direction of Paul Conrad. In the process, I had encountered "pseudo-convergent" sequences in an ordered group G, which are like Cauchy sequences, except that the differences be tween terms of large index approach not 0 but a convex subgroup G of G. If G is normal, then such sequences are conveniently described as Cauchy sequences in the quotient ordered group GIG. If G is not normal, of course GIG has no group structure, though it is still a totally ordered set. The best that can be said is that the elements of G permute GIG in an order-preserving fashion. In independent investigations around that time, both P. Conrad and P. Cohn had showed that a group admits a total right ordering if and only if the group is a group of automor phisms of a totally ordered set. (In a right ordered group, the order is required to be preserved by all right translations, unlike a (two-sided) ordered group, where both right and left translations must preserve the order.
Lattice Ordered Groups Advances And Techniques
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Author : Andrew Martin William Glass
language : en
Publisher:
Release Date : 1989
Lattice Ordered Groups Advances And Techniques written by Andrew Martin William Glass and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with categories.
Encyclopaedia Of Mathematics
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Author : M. Hazewinkel
language : en
Publisher: Springer
Release Date : 2013-12-01
Encyclopaedia Of Mathematics written by M. Hazewinkel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.