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In a bold and refreshingly informal style, this exciting text steers a middle course between elementary texts emphasizing connections with philosophy, logic, and electronic circuit design, and profound treatises aimed at advanced graduate students and professional mathematicians. It is written for readers who have studied at least two years of college-level mathematics. With carefully crafted prose, lucid explanations, and illuminating insights, it guides students to some of the deeper results of Boolean algebra --- and in particular to the important interconnections with topology --- without assuming a background in algebra, topology, and set theory. The parts of those subjects that are needed to understand the material are developed within the text itself. Highlights of the book include the normal form theorem; the homomorphism extension theorem; the isomorphism theorem for countable atomless Boolean algebras; the maximal ideal theorem; the celebrated Stone representation theorem; the existence and uniqueness theorems for canonical extensions and completions; Tarski’s isomorphism of factors theorem for countably complete Boolean algebras, and Hanf’s related counterexamples; and an extensive treatment of the algebraic-topological duality, including the duality between ideals and open sets, homomorphisms and continuous functions, subalgebras and quotient spaces, and direct products and Stone-Cech compactifications. A special feature of the book is the large number of exercises of varying levels of difficulty, from routine problems that help readers understand the basic definitions and theorems, to intermediate problems that extend or enrich material developed in the text, to harder problems that explore important ideas either not treated in the text, or that go substantially beyond its treatment. Hints for the solutions to the harder problems are given in an appendix. A detailed solutions manual for all exercises is available for instructors who adopt the text for a course.

Algebra, Boolean. --- Algebraic logic. --- Logic, Symbolic and mathematical --- Boolean algebra --- Boole's algebra --- Algebraic logic --- Set theory --- Booleaanse algebra. --- Boolesche Algebra. --- Boole, Algèbre de

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This handbook is the definitive compendium of the methods, results, and current initiatives in modern set theory in all its research directions. Set theory has entered its prime as an advanced and autonomous field of mathematics with foundational significance, and the expanse and variety of this handbook attests to the richness and sophistication of the subject. The chapters are written by acknowledged experts, major research figures in their areas, and they each bring to bear their experience and insights in carefully wrought, self-contained expositions. There is historical depth, elegant development, probing to the frontiers, and prospects for the future. This handbook is essential reading for the aspiring researcher, a pivotal focus for the veteran set theorist, and a massive reference for all those who want to gain a larger sense of the tremendous advances that have been made in the subject, one which first appeared as a foundation of mathematics but in the last several decades has expanded into a broad and far-reaching field with its own self-fueling initiatives.

Mathematics. --- Mathematical Logic and Foundations. --- Logic. --- Philosophy of Science. --- Science --- Logic, Symbolic and mathematical. --- Mathématiques --- Logique --- Sciences --- Logique symbolique et mathématique --- Philosophy. --- Philosophie --- Set theory. --- Harmonic spaces. --- Mappings (Mathematics). --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Mathematical Theory --- Algebra. --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Philosophy and science. --- Mathematical logic. --- Discrete mathematics. --- Discrete Mathematics. --- Mathematical analysis --- Logic, Symbolic and mathematical --- Set theory

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This book introduces the notions and methods of formal logic from a computer science standpoint, covering propositional logic, predicate logic, and foundations of logic programming. It presents applications and themes of computer science research such as resolution, automated deduction, and logic programming in a rigorous but readable way. The style and scope of the work, rounded out by the inclusion of exercises, make this an excellent textbook for an advanced undergraduate course in logic for computer scientists. This is a short introductory book on the topic of propositional and first-order logic, with a bias towards computer scientists…. Schöning decides to concentrate on computational issues, and gives us a short book (less than 170 pages) with a tight storyline…. I found this a nicely written book with many examples and exercises (126 of them). The presentation is natural and easy to follow…. This book seems suitable for a short course, a seminar series, or part of a larger course on Prolog and logic programming, probably at the advanced undergraduate level. — SIGACT News Contains examples and 126 interesting exercises which put the student in an active reading mode.... Would provide a good university short course introducing computer science students to theorem proving and logic programming. — Mathematical Reviews This book concentrates on those aspects of mathematical logic which have strong connections with different topics in computer science, especially automated deduction, logic programming, program verification and semantics of programming languages.... The numerous exercises and illustrative examples contribute a great extent to a better understanding of different concepts and results. The book can be successfully used as a handbook for an introductory course in artificial intelligence. — Zentralblatt MATH.

Programming --- Computer science --- Mathematical logic --- Logic, Symbolic and mathematical. --- Logic programming. --- Computer science. --- Mathematical Logic and Formal Languages. --- Mathematical Logic and Foundations. --- Algebra of logic --- Logic, Universal --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Informatics --- Science --- Mathematical logic. --- Logique mathématique --- Programmation logique --- Logique des prédicats

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Logic and Philosophy of Mathematics in the Early Husserl focuses on the first ten years of Edmund Husserl's work, from the publication of his Philosophy of Arithmetic (1891) to that of his Logical Investigations (1900/01), and aims to precisely locate his early work in the fields of logic, philosophy of logic and philosophy of mathematics. Unlike most phenomenologists, the author refrains from reading Husserl's early work as a more or less immature sketch of claims consolidated only in his later phenomenology, and unlike the majority of historians of logic she emphasizes the systematic strength and the originality of Husserl's logico-mathematical work. The book attempts to reconstruct the discussion between Husserl and those philosophers and mathematicians who contributed to new developments in logic, such as Leibniz, Bolzano, the logical algebraists (especially Boole and Schröder), Frege, and Hilbert and his school. It presents both a comprehensive critical examination of some of the major works produced by Husserl and his antagonists in the last decade of the 19th century and a formal reconstruction of many texts from Husserl's Nachlaß that have not yet been the object of systematical scrutiny. This volume will be of particular interest to researchers working in the history, and in the philosophy, of logic and mathematics, and more generally, to analytical philosophers and phenomenologists with a background in standard logic.

Logic, Symbolic and mathematical --- Mathematics --- Logic of mathematics --- Mathematics, Logic of --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Philosophy --- Husserl, Edmund, --- Husserl, Edmund --- Husserl, Edmond --- Logic --- Mathématiques --- Logique --- Philosophy. --- Philosophie --- EPUB-LIV-FT LIVHUMAI SPRINGER-B --- Husserl, Edmund (1859-1938) --- Mathématiques --- Philosophie de la logique --- Critique et interprétation

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Mathematical Logic for Computer Science is a mathematics textbook with theorems and proofs, but the choice of topics has been guided by the needs of students of computer science. The method of semantic tableaux provides an elegant way to teach logic that is both theoretically sound and easy to understand. The uniform use of tableaux-based techniques facilitates learning advanced logical systems based on what the student has learned from elementary systems. The logical systems presented are: propositional logic, first-order logic, resolution and its application to logic programming, Hoare logic for the verification of sequential programs, and linear temporal logic for the verification of concurrent programs. The third edition has been entirely rewritten and includes new chapters on central topics of modern computer science: SAT solvers and model checking. There are 150 exercises with answers available to qualified instructors. Documented, open-source, Prolog source code for the algorithms is available at http://code.google.com/p/mlcs/ Mordechai (Moti) Ben-Ari is with the Department of Science Teaching at the Weizmann Institute of Science. He is a Distinguished Educator of the ACM and has received the ACM/SIGCSE Award for Outstanding Contributions to Computer Science Education. His other textbooks published by Springer are: Ada for Software Engineers (Second Edition) and Principles of the Spin Model Checker.

Mathematical logic --- wiskunde --- Mathematical logic. --- Mathematical Logic and Formal Languages. --- Mathematical Logic and Foundations. --- Logic, Symbolic and mathematical. --- Computer logic --- Logique mathématique --- Logique informatique --- Algebra of logic --- Logic, Universal --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism