Download or read book Undecidable Theories written by Alfred Tarski and published by Elsevier. This book was released on 1953 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Undecidable Theories written by Alfred Tarski and published by Dover Books on Mathematics. This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This well-known book by the famed logician consists of three treatises: A General Method in Proofs of Undecidability, Undecidability and Essential Undecidability in Mathematics, and Undecidability of the Elementary Theory of Groups. 1953 edition.
Download or read book Undecidable Theories written by Alfred Tarski and published by . This book was released on 1968 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Decidable Theories written by Dirk Siefkes and published by Springer. This book was released on 2006-11-15 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: "We prove that any variety of relation algebras which contains an algebra with infinitely many elements below the identity, or which contains the full group relation algebra on some infinite group (or on arbitrarily large finite groups), must have an undecidable equational theory. Then we construct an embedding of the lattice of all subsets of the natural numbers into the lattice of varieties of relation algebras such that the variety correlated with a set [italic capital]X of natural numbers has a decidable equational theory if and only if [italic capital]X is a decidable (i.e., recursive) set. Finally, we construct an example of an infinite, finitely generated, simple, representable relation algebra that has a decidable equational theory.'' -- Abstract.
Download or read book Undecidable Theories written by Alfred Taski and published by . This book was released on 1973 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Theory of Models written by J.W. Addison and published by Elsevier. This book was released on 2014-05-27 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies in Logic and the Foundations of Mathematics: The Theory of Models covers the proceedings of the International Symposium on the Theory of Models, held at the University of California, Berkeley on June 25 to July 11, 1963. The book focuses on works devoted to the foundations of mathematics, generally known as "the theory of models." The selection first discusses the method of alternating chains, semantic construction of Lewis's systems S4 and S5, and continuous model theory. Concerns include ordered model theory, 2-valued model theory, semantics, sequents, axiomatization, formulas, axiomatic approach to hierarchies, alternating chains, and difference hierarchies. The text also ponders on Boolean notions extended to higher dimensions, elementary theories with models without automorphisms, and applications of the notions of forcing and generic sets. The manuscript takes a look at a hypothesis concerning the extension of finite relations and its verification for certain special cases, theories of functors and models, model-theoretic methods in the study of elementary logic, and extensions of relational structures. The text also reviews relatively categorical and normal theories, algebraic theories, categories, and functors, denumerable models of theories with extra predicates, and non-standard models for fragments of number theory. The selection is highly recommended for mathematicians and researchers interested in the theory of models.
Download or read book Computability Theory written by S. Barry Cooper and published by CRC Press. This book was released on 2017-09-06 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computability theory originated with the seminal work of Gödel, Church, Turing, Kleene and Post in the 1930s. This theory includes a wide spectrum of topics, such as the theory of reducibilities and their degree structures, computably enumerable sets and their automorphisms, and subrecursive hierarchy classifications. Recent work in computability theory has focused on Turing definability and promises to have far-reaching mathematical, scientific, and philosophical consequences. Written by a leading researcher, Computability Theory provides a concise, comprehensive, and authoritative introduction to contemporary computability theory, techniques, and results. The basic concepts and techniques of computability theory are placed in their historical, philosophical and logical context. This presentation is characterized by an unusual breadth of coverage and the inclusion of advanced topics not to be found elsewhere in the literature at this level. The book includes both the standard material for a first course in computability and more advanced looks at degree structures, forcing, priority methods, and determinacy. The final chapter explores a variety of computability applications to mathematics and science. Computability Theory is an invaluable text, reference, and guide to the direction of current research in the field. Nowhere else will you find the techniques and results of this beautiful and basic subject brought alive in such an approachable and lively way.
Download or read book Logics for Computer Science written by Anita Wasilewska and published by Springer. This book was released on 2018-11-03 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing an in-depth introduction to fundamental classical and non-classical logics, this textbook offers a comprehensive survey of logics for computer scientists. Logics for Computer Science contains intuitive introductory chapters explaining the need for logical investigations, motivations for different types of logics and some of their history. They are followed by strict formal approach chapters. All chapters contain many detailed examples explaining each of the introduced notions and definitions, well chosen sets of exercises with carefully written solutions, and sets of homework. While many logic books are available, they were written by logicians for logicians, not for computer scientists. They usually choose one particular way of presenting the material and use a specialized language. Logics for Computer Science discusses Gentzen as well as Hilbert formalizations, first order theories, the Hilbert Program, Godel's first and second incompleteness theorems and their proofs. It also introduces and discusses some many valued logics, modal logics and introduces algebraic models for classical, intuitionistic, and modal S4 and S5 logics. The theory of computation is based on concepts defined by logicians and mathematicians. Logic plays a fundamental role in computer science, and this book explains the basic theorems, as well as different techniques of proving them in classical and some non-classical logics. Important applications derived from concepts of logic for computer technology include Artificial Intelligence and Software Engineering. In addition to Computer Science, this book may also find an audience in mathematics and philosophy courses, and some of the chapters are also useful for a course in Artificial Intelligence.
Download or read book Uncertainty and Undecidability in Twentieth Century Literature and Literary Theory written by Mette Leonard Høeg and published by Taylor & Francis. This book was released on 2022-04-28 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: Undecidability is a fundamental quality of literature and constitutive of what renders some works appealing and engaging across time and in different contexts. This book explores the essential literary notion and its role, function and effect in late nineteenth- and twentieth-century literature and literary theory. The book traces the notion historically, providing a map of central theories addressing interpretative challenges and recalcitrance in literature and showing ‘theory of uncertainty’ to be an essential strand of literary theory. While uncertainty is present in all literature, and indeed a prerequisite for any stabilisation of meaning, the Modernist period is characterised by a particularly strong awareness of uncertainty and its subforms of undecidability, ambiguity, indeterminacy, etc. With examples from seminal Modernist works by Woolf, Proust, Ford, Kafka and Musil, the book sheds light on undecidability as a central structuring principle and guiding philosophical idea in twentieth-century literature and demonstrates the analytical value of undecidability as a critical concept and reading-strategy. Defining undecidability as a specific ‘sustained’ and ‘productive’ kind of uncertainty and distinguishing it from related forms, such as ambiguity, indeterminacy and indistinction, the book develops a systematic but flexible theory of undecidability and outlines a productive reading-strategy based on the recognition of textual and interpretive undecidability.
Download or read book Classical Mathematical Logic written by Richard L. Epstein and published by Princeton University Press. This book was released on 2006-07-23 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Classical Mathematical Logic, Richard L. Epstein relates the systems of mathematical logic to their original motivations to formalize reasoning in mathematics. The book also shows how mathematical logic can be used to formalize particular systems of mathematics. It sets out the formalization not only of arithmetic, but also of group theory, field theory, and linear orderings. These lead to the formalization of the real numbers and Euclidean plane geometry. The scope and limitations of modern logic are made clear in these formalizations. The book provides detailed explanations of all proofs and the insights behind the proofs, as well as detailed and nontrivial examples and problems. The book has more than 550 exercises. It can be used in advanced undergraduate or graduate courses and for self-study and reference. Classical Mathematical Logic presents a unified treatment of material that until now has been available only by consulting many different books and research articles, written with various notation systems and axiomatizations.
Download or read book On the Undecidability of Certain Finite Theories written by Solomon A. Garfunkel and published by . This book was released on 1967 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Modern Mathematics written by Helena Rasiowa and published by Elsevier. This book was released on 2014-05-12 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Modern Mathematics focuses on the operations, principles, and methodologies involved in modern mathematics. The monograph first tackles the algebra of sets, natural numbers, and functions. Discussions focus on groups of transformations, composition of functions, an axiomatic approach to natural numbers, intersection of sets, axioms of the algebra of sets, fields of sets, prepositional functions of one variable, and difference of sets. The text then takes a look at generalized unions and intersections of sets, Cartesian products of sets, and equivalence relations. The book ponders on powers of sets, ordered sets, and linearly ordered sets. Topics include isomorphism of linearly ordered sets, dense linear ordering, maximal and minimal elements, quasi-ordering relations, inequalities for cardinal numbers, sets of the power of the continuum, and Cantor's theorem. The manuscript then examines elementary concepts of abstract algebras, functional calculus and its applications in mathematical proofs, and propositional calculus and its applications in mathematical proofs. The publication is a valuable reference for mathematicians and researchers interested in modern mathematics.
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 The Classical Decision Problem written by Egon Börger and published by Springer Science & Business Media. This book was released on 2001-08-28 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive treatment of the classical decision problem of mathematical logic and of the role of the classical decision problem in modern computer science. The text presents a revealing analysis of the natural order of decidable and undecidable cases and includes a number of simple proofs and exercises.
Download or read book Description Logic Theory Combination and All That written by Carsten Lutz and published by Springer. This book was released on 2019-06-25 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Festschrift has been put together on the occasion of Franz Baader's 60th birthday to celebrate his fundamental and highly influential scientific contributions. The 30 papers in this volume cover several scientific areas that Franz Baader has been working on during the last three decades, including description logics, term rewriting, and the combination of decision procedures. We hope that readers will enjoy the articles gathered in Franz's honour and appreciate the breadth and depth of his favourite areas of computer science.
Download or read book Mathematical Theory and Computational Practice written by Klaus Ambos-Spies and published by Springer Science & Business Media. This book was released on 2009-07-15 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 5th Conference on Computability in Europe, CiE 2009, held in Heidelberg, Germany, during July 19-24, 2009. The 34 papers presented together with 17 invited lectures were carefully reviewed and selected from 100 submissions. The aims of the conference is to advance our theoretical understanding of what can and cannot be computed, by any means of computation. It is the largest international meeting focused on computability theoretic issues.
