A Friendly Introduction To Mathematical Logic

Author : Christopher C. Leary
Publisher : Lulu.com
ISBN 13 : 1942341075
Total Pages : 382 pages
Book Rating : 4.79/5 ( download)

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Download or read book A Friendly Introduction to Mathematical Logic written by Christopher C. Leary and published by Lulu.com. This book was released on 2015 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this expansion of Leary's user-friendly 1st edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study. Updating the 1st Edition's treatment of languages, structures, and deductions, leading to rigorous proofs of Gödel's First and Second Incompleteness Theorems, the expanded 2nd Edition includes a new introduction to incompleteness through computability as well as solutions to selected exercises.

Author : Richard E. Hodel
Publisher : Courier Corporation
ISBN 13 : 0486497852
Total Pages : 514 pages
Book Rating : 4.53/5 ( download)

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Download or read book An Introduction to Mathematical Logic written by Richard E. Hodel and published by Courier Corporation. This book was released on 2013-01-01 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive overview ofmathematical logic is designedprimarily for advanced undergraduatesand graduate studentsof mathematics. The treatmentalso contains much of interest toadvanced students in computerscience and philosophy. Topics include propositional logic;first-order languages and logic; incompleteness, undecidability,and indefinability; recursive functions; computability;and Hilbert’s Tenth Problem.Reprint of the PWS Publishing Company, Boston, 1995edition.

Author : Michal Walicki
Publisher : World Scientific Publishing Company
ISBN 13 : 9814719986
Total Pages : 304 pages
Book Rating : 4.88/5 ( download)

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Download or read book Introduction To Mathematical Logic (Extended Edition) written by Michal Walicki and published by World Scientific Publishing Company. This book was released on 2016-08-12 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a systematic and well-paced introduction to mathematical logic. Excellent as a course text, the book presupposes only elementary background and can be used also for self-study by more ambitious students.Starting with the basics of set theory, induction and computability, it covers propositional and first order logic — their syntax, reasoning systems and semantics. Soundness and completeness results for Hilbert's and Gentzen's systems are presented, along with simple decidability arguments. The general applicability of various concepts and techniques is demonstrated by highlighting their consistent reuse in different contexts.Unlike in most comparable texts, presentation of syntactic reasoning systems precedes the semantic explanations. The simplicity of syntactic constructions and rules — of a high, though often neglected, pedagogical value — aids students in approaching more complex semantic issues. This order of presentation also brings forth the relative independence of syntax from the semantics, helping to appreciate the importance of the purely symbolic systems, like those underlying computers.An overview of the history of logic precedes the main text, while informal analogies precede introduction of most central concepts. These informal aspects are kept clearly apart from the technical ones. Together, they form a unique text which may be appreciated equally by lecturers and students occupied with mathematical precision, as well as those interested in the relations of logical formalisms to the problems of computability and the philosophy of logic.This revised edition contains also, besides many new exercises, a new chapter on semantic paradoxes. An equivalence of logical and graphical representations allows us to see vicious circularity as the odd cycles in the graphical representation and can be used as a simple tool for diagnosing paradoxes in natural discourse.

Author : Paul C. Rosenbloom
Publisher : Courier Dover Publications
ISBN 13 : 9780486446172
Total Pages : 0 pages
Book Rating : 4.74/5 ( download)

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Download or read book The Elements of Mathematical Logic written by Paul C. Rosenbloom and published by Courier Dover Publications. This book was released on 2005 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: An excellent introduction to mathematical logic, this book provides readers with a sound knowledge of the most important approaches to the subject, stressing the use of logical methods in attacking nontrivial problems. Its chapters cover the logic of classes (including a section on the structure and representation of Boolean algebras, which are applied in the following chapters to the study of deductive systems), the logic of propositions, the logic of propositional functions (summarizing the methods of Russell, Quine, Zermelo, Curry, and Church for the construction of such logics), and the general syntax of language, with a brief introduction that also illustrates applications to so-called undecidability and incompleteness theorems. Other topics include the simple proof of the completeness of the theory of combinations, Church's theorem on the recursive unsolvability of the decision problem for the restricted function calculus, and the demonstrable properties of a formal system as a criterion for its acceptability.

Author : Herbert B. Enderton
Publisher : Elsevier
ISBN 13 : 0080496466
Total Pages : 330 pages
Book Rating : 4.67/5 ( download)

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Download or read book A Mathematical Introduction to Logic written by Herbert B. Enderton and published by Elsevier. This book was released on 2001-01-23 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Mathematical Introduction to Logic

Author : George Tourlakis
Publisher : John Wiley & Sons
ISBN 13 : 1118030699
Total Pages : 314 pages
Book Rating : 4.91/5 ( download)

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Download or read book Mathematical Logic written by George Tourlakis and published by John Wiley & Sons. This book was released on 2011-03-01 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive and user-friendly guide to the use of logic in mathematical reasoning Mathematical Logic presents a comprehensive introduction to formal methods of logic and their use as a reliable tool for deductive reasoning. With its user-friendly approach, this book successfully equips readers with the key concepts and methods for formulating valid mathematical arguments that can be used to uncover truths across diverse areas of study such as mathematics, computer science, and philosophy. The book develops the logical tools for writing proofs by guiding readers through both the established "Hilbert" style of proof writing, as well as the "equational" style that is emerging in computer science and engineering applications. Chapters have been organized into the two topical areas of Boolean logic and predicate logic. Techniques situated outside formal logic are applied to illustrate and demonstrate significant facts regarding the power and limitations of logic, such as: Logic can certify truths and only truths. Logic can certify all absolute truths (completeness theorems of Post and Gödel). Logic cannot certify all "conditional" truths, such as those that are specific to the Peano arithmetic. Therefore, logic has some serious limitations, as shown through Gödel's incompleteness theorem. Numerous examples and problem sets are provided throughout the text, further facilitating readers' understanding of the capabilities of logic to discover mathematical truths. In addition, an extensive appendix introduces Tarski semantics and proceeds with detailed proofs of completeness and first incompleteness theorems, while also providing a self-contained introduction to the theory of computability. With its thorough scope of coverage and accessible style, Mathematical Logic is an ideal book for courses in mathematics, computer science, and philosophy at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers and practitioners who wish to learn how to use logic in their everyday work.

Author : Peter G. Hinman
Publisher : CRC Press
ISBN 13 : 1439864276
Total Pages : 894 pages
Book Rating : 4.72/5 ( download)

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Download or read book Fundamentals of Mathematical Logic written by Peter G. Hinman and published by CRC Press. This book was released on 2018-10-08 with total page 894 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory graduate text covers modern mathematical logic from propositional, first-order and infinitary logic and Gödel's Incompleteness Theorems to extensive introductions to set theory, model theory and recursion (computability) theory. Based on the author's more than 35 years of teaching experience, the book develops students' intuition by presenting complex ideas in the simplest context for which they make sense. The book is appropriate for use as a classroom text, for self-study, and as a reference on the state of modern logic.

Author : Alonzo Church
Publisher :
ISBN 13 :
Total Pages : 142 pages
Book Rating : 4.00/5 ( download)

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Download or read book Introduction to Mathematical Logic written by Alonzo Church and published by . This book was released on 1965 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Wolfgang Rautenberg
Publisher : Springer Science & Business Media
ISBN 13 : 0387342419
Total Pages : 273 pages
Book Rating : 4.12/5 ( download)

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Download or read book A Concise Introduction to Mathematical Logic written by Wolfgang Rautenberg and published by Springer Science & Business Media. This book was released on 2006-09-28 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: While there are already several well known textbooks on mathematical logic this book is unique in treating the material in a concise and streamlined fashion. This allows many important topics to be covered in a one semester course. Although the book is intended for use as a graduate text the first three chapters can be understood by undergraduates interested in mathematical logic. The remaining chapters contain material on logic programming for computer scientists, model theory, recursion theory, Godel’s Incompleteness Theorems, and applications of mathematical logic. Philosophical and foundational problems of mathematics are discussed throughout the text.

Author : Ian Chiswell
Publisher : OUP Oxford
ISBN 13 : 0191524808
Total Pages : 258 pages
Book Rating : 4.06/5 ( download)

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Download or read book Mathematical Logic written by Ian Chiswell and published by OUP Oxford. This book was released on 2007-05-18 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assuming no previous study in logic, this informal yet rigorous text covers the material of a standard undergraduate first course in mathematical logic, using natural deduction and leading up to the completeness theorem for first-order logic. At each stage of the text, the reader is given an intuition based on standard mathematical practice, which is subsequently developed with clean formal mathematics. Alongside the practical examples, readers learn what can and can't be calculated; for example the correctness of a derivation proving a given sequent can be tested mechanically, but there is no general mechanical test for the existence of a derivation proving the given sequent. The undecidability results are proved rigorously in an optional final chapter, assuming Matiyasevich's theorem characterising the computably enumerable relations. Rigorous proofs of the adequacy and completeness proofs of the relevant logics are provided, with careful attention to the languages involved. Optional sections discuss the classification of mathematical structures by first-order theories; the required theory of cardinality is developed from scratch. Throughout the book there are notes on historical aspects of the material, and connections with linguistics and computer science, and the discussion of syntax and semantics is influenced by modern linguistic approaches. Two basic themes in recent cognitive science studies of actual human reasoning are also introduced. Including extensive exercises and selected solutions, this text is ideal for students in Logic, Mathematics, Philosophy, and Computer Science.