Decidability and Boolean Representations PDF Download

Author: Stanley Burris
Publisher: American Mathematical Soc.
ISBN: 0821822462
Category : Mathematics
Languages : en
Pages : 106

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Author: A.G. Pinus
Publisher: Springer Science & Business Media
ISBN: 9401709386
Category : Mathematics
Languages : en
Pages : 357

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During the last few decades the ideas, methods, and results of the theory of Boolean algebras have played an increasing role in various branches of mathematics and cybernetics. This monograph is devoted to the fundamentals of the theory of Boolean constructions in universal algebra. Also considered are the problems of presenting different varieties of universal algebra with these constructions, and applications for investigating the spectra and skeletons of varieties of universal algebras. For researchers whose work involves universal algebra and logic.

Author: Ralph McKenzie
Publisher: Springer Science & Business Media
ISBN: 9780817634391
Category : Mathematics
Languages : en
Pages : 232

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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.

Author: Heinz-Dieter Ebbinghaus
Publisher: Springer Science & Business Media
ISBN: 3662090589
Category : Mathematics
Languages : en
Pages : 653

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Gert H. Müller The growth of the number of publications in almost all scientific areas, as in the area of (mathematical) logic, is taken as a sign of our scientifically minded culture, but it also has a terrifying aspect. In addition, given the rapidly growing sophistica tion, specialization and hence subdivision of logic, researchers, students and teachers may have a hard time getting an overview of the existing literature, partic ularly if they do not have an extensive library available in their neighbourhood: they simply do not even know what to ask for! More specifically, if someone vaguely knows that something vaguely connected with his interests exists some where in the literature, he may not be able to find it even by searching through the publications scattered in the review journals. Answering this challenge was and is the central motivation for compiling this Bibliography. The Bibliography comprises (presently) the following six volumes (listed with the corresponding Editors): I. Classical Logic W. Rautenberg 11. Non-classical Logics W. Rautenberg 111. Model Theory H.-D. Ebbinghaus IV. Recursion Theory P.G. Hinman V. Set Theory A.R. Blass VI. ProofTheory; Constructive Mathematics J.E. Kister; D. van Dalen & A.S. Troelstra.

Author: Sergey Goncharov
Publisher: Springer Science & Business Media
ISBN: 9780306110610
Category : Mathematics
Languages : en
Pages : 344

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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.

Author: Jacek Malinowski
Publisher: Springer Nature
ISBN: 3031444906
Category :
Languages : en
Pages : 473

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Author: Juha Oikkonen
Publisher: Cambridge University Press
ISBN: 110716902X
Category : Mathematics
Languages : en
Pages : 316

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The proceedings of the Association for Symbolic Logic meeting held in Helsinki, Finland, in July 1990, containing eighteen papers written by leading researchers in logic. Between them they cover all fields of mathematical logic, including model theory, proof theory, recursion theory, and set theory.

Author: R.S. Freese
Publisher: Springer
ISBN: 3540409548
Category : Mathematics
Languages : en
Pages : 314

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Author: Bradd T. Hart
Publisher: Springer Science & Business Media
ISBN: 9401589232
Category : Mathematics
Languages : en
Pages : 285

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Recent major advances in model theory include connections between model theory and Diophantine and real analytic geometry, permutation groups, and finite algebras. The present book contains lectures on recent results in algebraic model theory, covering topics from the following areas: geometric model theory, the model theory of analytic structures, permutation groups in model theory, the spectra of countable theories, and the structure of finite algebras. Audience: Graduate students in logic and others wishing to keep abreast of current trends in model theory. The lectures contain sufficient introductory material to be able to grasp the recent results presented.

Author: Alain Finkel
Publisher: Springer Science & Business Media
ISBN: 9783540552109
Category : Computers
Languages : en
Pages : 644

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This volume gives the proceedings of the ninth Symposium on Theoretical Aspects of Computer Science (STACS). This annual symposium is held alternately in France and Germany and is organized jointly by the Special Interest Group for Fundamental Computer Science of the Association Francaise des Sciences et Technologies de l'Information et des Syst mes (AFCET) and the Special Interest Group for Theoretical Computer Science of the Gesellschaft f}r Informatik (GI). The volume includes three invited lectures and sections on parallel algorithms, logic and semantics, computational geometry, automata and languages, structural complexity, computational geometry and learning theory, complexity and communication, distributed systems, complexity, algorithms, cryptography, VLSI, words and rewriting, and systems.