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Author: Octavio Carlos García Publisher: American Mathematical Soc. ISBN: 0821823086 Category : Mathematics Languages : en Pages : 133
Book Description
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.
Author: Octavio Carlos García Publisher: American Mathematical Soc. ISBN: 0821823086 Category : Mathematics Languages : en Pages : 133
Book Description
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.
Author: Jan Mycielski Publisher: American Mathematical Soc. ISBN: 0821824880 Category : First-order logic Languages : en Pages : 78
Book Description
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.
Author: Ivo G. Rosenberg Publisher: Springer Science & Business Media ISBN: 9401706972 Category : Mathematics Languages : en Pages : 565
Book Description
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.
Author: Ralph S. Freese Publisher: American Mathematical Society ISBN: 1470467976 Category : Mathematics Languages : en Pages : 496
Book Description
This book is the second 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.
Author: Keith Kearnes Publisher: American Mathematical Soc. ISBN: 0821883232 Category : Mathematics Languages : en Pages : 183
Book Description
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.
Author: Klaus Denecke Publisher: CRC Press ISBN: 9789056992354 Category : Mathematics Languages : en Pages : 334
Book Description
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 general theory to partial algebras. The last chapter contains exercises and open problems with suggestions for future work in this area of research. Graduate students and mathematical researchers will find Hyperidentities and Clones a thought-provoking and illuminating text that offers a unique opportunity to study the topic in one source.
Author: Octavio Carlos García
Author: Octavio Carlos García
Author: Octavio Carlos García
Author: Jan Mycielski
Author: Ivo G. Rosenberg
Author: Ralph S. Freese
Author: Keith Kearnes
Author: Klaus Denecke
Author: Octavio Carlos García
Author: Stephen D. Comer
Author: Leonid A. Bokut'