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Hyperidentities and Clones

2000-08-08 Mathematics
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Release : 2000-08-08
Genre : Mathematics
Kind : eBook
Book Rating : 51X/5 ( reviews)

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Book Synopsis Hyperidentities and Clones by : Klaus Denecke

Download or read book Hyperidentities and Clones written by Klaus Denecke. This book was released on 2000-08-08. Available in PDF, EPUB and Kindle. Book excerpt: 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

Hyperidentities and Clones

2000-08-08 Mathematics
Download Hyperidentities and Clones PDF Online Free

Author :
Release : 2000-08-08
Genre : Mathematics
Kind : eBook
Book Rating : 354/5 ( reviews)

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Book Synopsis Hyperidentities and Clones by : Klaus Denecke

Download or read book Hyperidentities and Clones written by Klaus Denecke. This book was released on 2000-08-08. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Clones and Hyperidentities

1996
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Release : 1996
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Book Rating : /5 ( reviews)

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Book Synopsis Clones and Hyperidentities by : Klaus Denecke

Download or read book Clones and Hyperidentities written by Klaus Denecke. This book was released on 1996. Available in PDF, EPUB and Kindle. Book excerpt:

Hyperidentities: Boolean And De Morgan Structures

2022-09-20 Mathematics
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Release : 2022-09-20
Genre : Mathematics
Kind : eBook
Book Rating : 931/5 ( reviews)

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Book Synopsis Hyperidentities: Boolean And De Morgan Structures by : Yuri Movsisyan

Download or read book Hyperidentities: Boolean And De Morgan Structures written by Yuri Movsisyan. This book was released on 2022-09-20. Available in PDF, EPUB and Kindle. Book excerpt: Hyperidentities are important formulae of second-order logic, and research in hyperidentities paves way for the study of second-order logic and second-order model theory.This book illustrates many important current trends and perspectives for the field of hyperidentities and their applications, of interest to researchers in modern algebra and discrete mathematics. It covers a number of directions, including the characterizations of the Boolean algebra of n-ary Boolean functions and the distributive lattice of n-ary monotone Boolean functions; the classification of hyperidentities of the variety of lattices, the variety of distributive (modular) lattices, the variety of Boolean algebras, and the variety of De Morgan algebras; the characterization of algebras with aforementioned hyperidentities; the functional representations of finitely-generated free algebras of various varieties of lattices and bilattices via generalized Boolean functions (De Morgan functions, quasi-De Morgan functions, super-Boolean functions, super-De Morgan functions, etc); the structural results for De Morgan algebras, Boole-De Morgan algebras, super-Boolean algebras, bilattices, among others.While problems of Boolean functions theory are well known, the present book offers alternative, more general problems, involving the concepts of De Morgan functions, quasi-De Morgan functions, super-Boolean functions, and super-De Morgan functions, etc. In contrast to other generalized Boolean functions discovered and investigated so far, these functions have clearly normal forms. This quality is of crucial importance for their applications in pure and applied mathematics, especially in discrete mathematics, quantum computation, quantum information theory, quantum logic, and the theory of quantum computers.

Algebras and Orders

2013-03-09 Mathematics
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Release : 2013-03-09
Genre : Mathematics
Kind : eBook
Book Rating : 972/5 ( reviews)

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Book Synopsis Algebras and Orders by : Ivo G. Rosenberg

Download or read book Algebras and Orders written by Ivo G. Rosenberg. This book was released on 2013-03-09. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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