Download or read book On the Decidability of the Theory of Boolean Algebras written by Evelyn Ingrid Meierholzner and published by . This book was released on 1983 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Decidability and Boolean Representations written by Stanley Burris and published by American Mathematical Soc.. This book was released on 1981 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: In part I we address the question: which varieties have a decidable first order theory? We confine our attention to varieties whose algebras have modular congruence lattices (i.e., modular varieties), and focus primarily on locally finite varieties, although near the end of the paper Zamjatin's description of all decidable varieties of groups and rings, and offer a new proof of it. In part II, we show that if a variety admits such sheaf representations using only finitely many stalks, all of which are finite, then the variety can be decomposed in the product of a discriminator variety and an abelian variety. We continue this investigation by looking at well-known specializations of the sheaf construction, namely Boolean powers and sub-Boolean powers, giving special emphasis to quasi-primal algebras A, such that the sub-Boolean powers of A form a variety (this extends the work of Arens and Kaplansky on finite fields).
Download or read book Countable Boolean Algebras and Decidability written by Sergey Goncharov and published by Springer Science & Business Media. This book was released on 1997-01-31 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the latest Russian research covering the structure and algorithmic properties of Boolean algebras from the algebraic and model-theoretic points of view. A significantly revised version of the author's Countable Boolean Algebras (Nauka, Novosibirsk, 1989), the text presents new results as well as a selection of open questions on Boolean algebras. Other current features include discussions of the Kottonen algebras in enrichments by ideals and automorphisms, and the properties of the automorphism groups.
Download or read book Handbook of Boolean Algebras written by Sabine Koppelberg and published by . This book was released on 1989 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Decidable Theories written by J.R. Büchi and published by Springer. This book was released on 2006-11-14 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Undecidable extensions of the theory of Boolean algebras written by Martin Weese and published by . This book was released on 1984 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Topics in the Theory of Arithmetical Classes and Boolean Algebras written by Robert Lawson Vaught and published by . This book was released on 1954 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Structure of Decidable Locally Finite Varieties written by Ralph McKenzie and published by Springer Science & Business Media. This book was released on 1989-11-01 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: A mathematically precise definition of the intuitive notion of "algorithm" was implicit in Kurt Godel's [1931] paper on formally undecidable propo sitions of arithmetic. During the 1930s, in the work of such mathemati cians as Alonzo Church, Stephen Kleene, Barkley Rosser and Alfred Tarski, Godel's idea evolved into the concept of a recursive function. Church pro posed the thesis, generally accepted today, that an effective algorithm is the same thing as a procedure whose output is a recursive function of the input (suitably coded as an integer). With these concepts, it became possible to prove that many familiar theories are undecidable (or non-recursive)-i. e. , that there does not exist an effective algorithm (recursive function) which would allow one to determine which sentences belong to the theory. It was clear from the beginning that any theory with a rich enough mathematical content must be undecidable. On the other hand, some theories with a substantial content are decidable. Examples of such decidabLe theories are the theory of Boolean algebras (Tarski [1949]), the theory of Abelian groups (Szmiele~ [1955]), and the theories of elementary arithmetic and geometry (Tarski [1951]' but Tarski discovered these results around 1930). The de termination of precise lines of division between the classes of decidable and undecidable theories became an important goal of research in this area. algebra we mean simply any structure (A, h(i E I)} consisting of By an a nonvoid set A and a system of finitary operations Ii over A.
Download or read book Handbook of Boolean Algebras written by James Donald Monk and published by . This book was released on 1989 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Boolean Algebras written by Roman Sikorski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are two aspects to the theory of Boolean algebras; the algebraic and the set-theoretical. A Boolean algebra can be considered as a special kind of algebraic ring, or as a generalization of the set-theoretical notion of a field of sets. Fundamental theorems in both of these directions are due to M. H. STONE, whose papers have opened a new era in the develop ment of this theory. This work treats the set-theoretical aspect, with little mention being made of the algebraic one. The book is composed of two chapters and an appendix. Chapter I is devoted to the study of Boolean algebras from the point of view of finite Boolean operations only; a greater part of its contents can be found in the books of BIRKHOFF [2J and HERMES [1]. Chapter II seems to be the first systematic study of Boolean algebras with infinite Boolean operations. To understand Chapters I and II it suffices only to know fundamental notions from general set theory and set-theoretical topology. No know ledge of lattice theory or of abstract algebra is presumed. Less familiar topological theorems are recalled, and only a few examples use more advanced topological means; but these may be omitted. All theorems in both chapters are given with full proofs.
Download or read book Lectures on Boolean Algebras written by Paul R. Halmos and published by Courier Dover Publications. This book was released on 2018-09-12 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise and informal as well as systematic, this presentation on the basics of Boolean algebra has ranked among the fundamental books on the subject since its initial publication in 1963.
Download or read book Introduction to Boolean Algebras written by Steven Givant and published by Springer Science & Business Media. This book was released on 2008-12-02 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an informal though systematic series of lectures on Boolean algebras. It contains background chapters on topology and continuous functions and includes hundreds of exercises as well as a solutions manual.
Download or read book Enumerability Decidability Computability written by Hans Hermes and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Once we have accepted a precise replacement of the concept of algo rithm, it becomes possible to attempt the problem whether there exist well-defined collections of problems which cannot be handled by algo rithms, and if that is the case, to give concrete cases of this kind. Many such investigations were carried out during the last few decades. The undecidability of arithmetic and other mathematical theories was shown, further the unsolvability of the word problem of group theory. Many mathematicians consider these results and the theory on which they are based to be the most characteristic achievements of mathe matics in the first half of the twentieth century. If we grant the legitimacy of the suggested precise replacements of the concept of algorithm and related concepts, then we can say that the mathematicians have shown by strictly mathematical methods that there exist mathematical problems which cannot be dealt with by the methods of calculating mathematics. In view of the important role which mathematics plays today in our conception of the world this fact is of great philosophical interest. Post speaks of a natural law about the "limitations of the mathematicizing power of Homo Sapiens". Here we also find a starting point for the discussion of the question, what the actual creative activity of the mathematician consists in. In this book we shall give an introduction to the theory of algorithms.
Download or read book On the Theory of Boolean Formulas written by E. W. Samson and published by . This book was released on 1965 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of substitutions for Boolean formulas developed in a previous report is applied here to the determination of those s-tuples of formulas that may be allowable replacements for s -tuples of sub-formulas of given Boolean formulas. The criteria of allowability are very general and flexible, yet may be expressed with great precision and ease. The results formalize and extend various known isolated instances. They may be used for the study of a large number of problems in the theory and application of Boolean formulas and functions.
Download or read book Decision Problems for Equational Theories of Relation Algebras written by H. Andréka and published by American Mathematical Soc.. This book was released on 1997-01-01 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents a systematic study of decision problems for equational theories of algebras of binary relations (relation algebras). For example, an easily applicable but deep method, based on von Neumann's coordinatization theorem, is developed for establishing undecidability results. The method is used to solve several outstanding problems posed by Tarski. In addition, the complexity of intervals of equational theories of relation algebras with respect to questions of decidability is investigated. Using ideas that go back to Jonsson and Lyndon, the authors show that such intervals can have the same complexity as the lattice of subsets of the set of the natural numbers. Finally, some new and quite interesting examples of decidable equational theories are given. The methods developed in the monograph show promise of broad applicability. The provide researchers in algebra and logc with a new arsenal of techniques for resolving decision questions in various domains of algebraic logic.
Download or read book Boolean Algebra Essentials written by Alan Solomon and published by Research & Education Assoc.. This book was released on 2013-01-01 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: REA’s Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Boolean Algebra includes set theory, sentential calculus, fundamental ideas of Boolean algebras, lattices, rings and Boolean algebras, the structure of a Boolean algebra, and Boolean algebra in communication systems.
Download or read book Sheaves of Algebras over Boolean Spaces written by Arthur Knoebel and published by Springer Science & Business Media. This book was released on 2011-12-15 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique monograph building bridges among a number of different areas of mathematics such as algebra, topology, and category theory. The author uses various tools to develop new applications of classical concepts. Detailed proofs are given for all major theorems, about half of which are completely new. Sheaves of Algebras over Boolean Spaces will take readers on a journey through sheaf theory, an important part of universal algebra. This excellent reference text is suitable for graduate students, researchers, and those who wish to learn about sheaves of algebras.
