Praise for the First Edition ". . . an enchanting book for those people in computer science or mathematics who are fascinated by the concept of infinity."—Computing Reviews ". . . a very well written introduction to set theory . . . easy ... The book concludes with an outline of Godel's incompleteness theorem. Ideal for a one-semester course, this concise text offers more detail and mathematically relevant examples than those available in elementary books on logic. First English translation of revolutionary paper (1931) that established that even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. Introduction by R. B. Braithwaite. Introduction to proof theory and its applications in mathematical logic, theoretical computer science and artificial intelligence. Found insideThis book takes the reader on a journey through Ramsey theory, from graph theory and combinatorics to set theory to logic and metamathematics. Found inside" There are 31 chapters in 5 parts and approximately 320 exercises marked by difficulty and whether or not they are necessary for further work in the book. Found inside – Page iThis book was written to serve as an introduction to logic, with in each chapter – if applicable – special emphasis on the interplay between logic and philosophy, mathematics, language and (theoretical) computer science. This lucid, non-intimidating presentation by a Russian scholar explores propositional logic, propositional calculus, and predicate logic. The book also considers the historical and philosophical context of these issues and their philosophical and methodological consequences. This work makes available to readers without specialized training in mathematics complete proofs of the fundamental metatheorems of standard (i.e., basically truth-functional) first order logic. Contents include an elementary but thorough overview of mathematical logic of 1st order; formal number theory; surveys of the work by Church, Turing, and others, including Gödel's completeness theorem, Gentzen's theorem, more. Stephen Cole Kleene was one of the greatest logicians of the twentieth century and this book is the influential textbook he wrote to teach the subject to the next generation. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras ... Consequently the book, while making an attractive first textbook for those who plan to specialise in logic, will be particularly valuable for mathematics and computer scientists whose primary interests lie elsewhere. Found inside – Page ivThis book treats the most important material in a concise and streamlined fashion. The third edition is a thorough and expanded revision of the former. Found insideThis volume, the third publication in the Perspectives in Logic series, is a much-needed monograph on the metamathematics of first-order arithmetic. Exercises appear throughout. Alfred Tarski, one of the greatest logicians of all time, is widely thought of as 'the man who defined truth'. The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. Describes the use of computer programs to check several proofs in the foundations of mathematics. Found insideChapter 6 is devoted to this topic; it contains the basic facts on the structure of derivations, both classically and intuitionistically. Finally, this edition contains a new chapter on Gödel's first incompleteness theorem. Finally there's an easy-to-follow book that will help readers succeed in the art of proving theorems. Sibley not only conveys the spirit of mathematics but also uncovers the skills required to succeed. Found insideThis volume offers insights into the development of mathematical logic over the last century. This work explores in historical depth the relation between philosophical quandaries of self-reference and recent 20th-century metamathematical notions of consistency and incompleteness. Table of contents Found insideThe book then explores the formal axiom system of Zermelo and Fraenkel before concluding with an extensive list of suggestions for further study. This comprehensive overview ofmathematical logic is designedprimarily for advanced undergraduatesand graduate studentsof mathematics. Found insideThis book presents a systematic treatment of deductive aspects and structures of fuzzy logic understood as many valued logic sui generis. This book explains the Metamath language and program, with specific emphasis on the fundamentals of the MPE database. Found insideThere are many exercises, and they provide the outline of what amounts to a second book that goes into all topics in more depth. This book has played a role in the education of many mature and accomplished researchers. It presents a comprehensive introduction to the theory, practice, and management of performance and quality improvement processes in healthcare organizations. The Unknowable is a very readable introduction to Chaitins ideas, and includes software (on the authors website) that will enable users to interact with the authors proofs. This work is a sequel to the author's Gödel's Incompleteness Theorems, though it can be read independently by anyone familiar with Gödel's incompleteness theorem for Peano arithmetic. Logical relativism is a pluralism according to which validity and logical consequence are relative to something. Stewart Shapiro explores various such views. This classic undergraduate treatment examines the deductive method in its first part and explores applications of logic and methodology in constructing mathematical theories in its second part. Exercises appear throughout. Found insideThis concise book provides a systematic, accessible introduction to the field that is trying to answer that question: the philosophy of mathematics. Øystein Linnebo, one of the world's leading scholars on the subject, introduces all of the ... The book first offers information on the dialectic of the relation between mathematical and metamathematical aspects; metamathematico-mathematical parallelism and its natural limits; practical applications of methods of mathematical logic; ... DIVBeginning with perspectives on the finite universe and classes and Aristotelian logic, the author examines permutations, combinations, and infinite cardinalities; numbering the continuum; Cantor's transfinite paradise; axiomatic set ... 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