The Lattice Of Interpretability Types Of Varieties
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The Lattice Of Interpretability Types Of Varieties
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Author : Octavio Carlos García
language : en
Publisher: American Mathematical Soc.
Release Date : 1984
The Lattice Of Interpretability Types Of Varieties written by Octavio Carlos García and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
We investigate the lattice, invented by W. D. Neumann in 1974, formed by the class of all varieties under the quasi-ordering "[script]V is interpretable in [script]W." The lattice is found to be non-modular and a proper class. Various familiar varieties are found to be [logical conjunction symbol {up arrow}]-irreducible (or prime) and various filters (especially Mal'tsev classes) are found to be indecomposable (or prime). Many familiar varieties are found to be inequivalent in the lattice, using a new technique of SIN algebras. Seven figures are included which document the known relationships between some sixty known or easily describable varieties and varietal families.
The Lattice Of Interpretability Types Of Varieties
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Author : Octavio Carlos García
language : en
Publisher:
Release Date : 1984
The Lattice Of Interpretability Types Of Varieties written by Octavio Carlos García and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Categories categories.
The Lattice Of Interpretability Types Of Varieties
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Author : Octavio Carlos García
language : en
Publisher: Amer Mathematical Society
Release Date : 2005-10-06
The Lattice Of Interpretability Types Of Varieties written by Octavio Carlos García and has been published by Amer Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-10-06 with Mathematics categories.
Algebras Lattices Varieties
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Author : Ralph S. Freese
language : en
Publisher: American Mathematical Society
Release Date : 2022-11-03
Algebras Lattices Varieties written by Ralph S. Freese and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-03 with Mathematics categories.
This book is the third of a three-volume set of books on the theory of algebras, a study that provides a consistent framework for understanding algebraic systems, including groups, rings, modules, semigroups and lattices. Volume I, first published in the 1980s, built the foundations of the theory and is considered to be a classic in this field. The long-awaited volumes II and III are now available. Taken together, the three volumes provide a comprehensive picture of the state of art in general algebra today, and serve as a valuable resource for anyone working in the general theory of algebraic systems or in related fields. The two new volumes are arranged around six themes first introduced in Volume I. Volume II covers the Classification of Varieties, Equational Logic, and Rudiments of Model Theory, and Volume III covers Finite Algebras and their Clones, Abstract Clone Theory, and the Commutator. These topics are presented in six chapters with independent expositions, but are linked by themes and motifs that run through all three volumes.
A Lattice Of Chapters Of Mathematics Interpretations Between Theorems
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Author : Jan Mycielski
language : en
Publisher: American Mathematical Soc.
Release Date : 1990
A Lattice Of Chapters Of Mathematics Interpretations Between Theorems written by Jan Mycielski and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
What are mathematical theories? What mathematical objects should correspond to this informal concept? The classical and most important answer to these questions is: Theories formalized in first order logic. But this answer has also some undesirable features. One of theme is the dependence of such theories upon the language or the choice of primitive concepts, whereas a slightly deeper view would identify theories interpretable in each other. The purpose of the present memoir is to investigate further, to survey the former work and to point out a number of open problems about local interpretability.
Algebras Lattices Varieties
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Author : Ralph N. McKenzie
language : en
Publisher: American Mathematical Society
Release Date : 2018-07-09
Algebras Lattices Varieties written by Ralph N. McKenzie and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-09 with Mathematics categories.
This book presents the foundations of a general theory of algebras. Often called “universal algebra”, this theory provides a common framework for all algebraic systems, including groups, rings, modules, fields, and lattices. Each chapter is replete with useful illustrations and exercises that solidify the reader's understanding. The book begins by developing the main concepts and working tools of algebras and lattices, and continues with examples of classical algebraic systems like groups, semigroups, monoids, and categories. The essence of the book lies in Chapter 4, which provides not only basic concepts and results of general algebra, but also the perspectives and intuitions shared by practitioners of the field. The book finishes with a study of possible uniqueness of factorizations of an algebra into a direct product of directly indecomposable algebras. There is enough material in this text for a two semester course sequence, but a one semester course could also focus primarily on Chapter 4, with additional topics selected from throughout the text.
Algebras And Orders
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Author : Ivo G. Rosenberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Algebras And Orders written by Ivo G. Rosenberg 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 2013-03-09 with Mathematics categories.
In the summer of 1991 the Department of Mathematics and Statistics of the Universite de Montreal was fortunate to host the NATO Advanced Study Institute "Algebras and Orders" as its 30th Seminaire de mathematiques superieures (SMS), a summer school with a long tradition and well-established reputation. This book contains the contributions of the invited speakers. Universal algebra- which established itself only in the 1930's- grew from traditional algebra (e.g., groups, modules, rings and lattices) and logic (e.g., propositional calculus, model theory and the theory of relations). It started by extending results from these fields but by now it is a well-established and dynamic discipline in its own right. One of the objectives of the ASI was to cover a broad spectrum of topics in this field, and to put in evidence the natural links to, and interactions with, boolean algebra, lattice theory, topology, graphs, relations, automata, theoretical computer science and (partial) orders. The theory of orders is a relatively young and vigorous discipline sharing certain topics as well as many researchers and meetings with universal algebra and lattice theory. W. Taylor surveyed the abstract clone theory which formalizes the process of compos ing operations (i.e., the formation of term operations) of an algebra as a special category with countably many objects, and leading naturally to the interpretation and equivalence of varieties.
The Shape Of Congruence Lattices
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Author : Keith Kearnes
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-02-26
The Shape Of Congruence Lattices written by Keith Kearnes and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-26 with Mathematics categories.
This monograph is concerned with the relationships between Maltsev conditions, commutator theories and the shapes of congruence lattices in varieties of algebras. The authors develop the theories of the strong commutator, the rectangular commutator, the strong rectangular commutator, as well as a solvability theory for the nonmodular TC commutator. They prove that a residually small variety that satisfies a congruence identity is congruence modular.
Hyperidentities And Clones
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Author : Klaus Denecke
language : en
Publisher: CRC Press
Release Date : 2000-08-08
Hyperidentities And Clones written by Klaus Denecke and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-08-08 with Mathematics categories.
Theories and results on hyperidentities have been published in various areas of the literature over the last 18 years. Hyperidentities and Clones integrates these into a coherent framework for the first time. The author also includes some applications of hyperidentities to the functional completeness problem in multiple-valued logic and extends the
Universal Algebra And Lattice Theory
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Author : Stephen D. Comer
language : en
Publisher: Springer
Release Date : 2006-12-08
Universal Algebra And Lattice Theory written by Stephen D. Comer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Mathematics categories.