A Beginner S Further Guide To Mathematical Logic

Author : Raymond Smullyan
Publisher : World Scientific Publishing Company
Page : 288 pages
File Size : 51,9 Mb
Release : 2016-11-11
Category : Electronic
ISBN : 9789814733014

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A Beginner's Further Guide to Mathematical Logic by Raymond Smullyan Pdf

This is the final book written by the late great puzzle master and logician, Dr. Raymond Smullyan. This book is a sequel to my Beginner's Guide to Mathematical Logic. The previous volume deals with elements of propositional and first-order logic, contains a bit on formal systems and recursion, and concludes with chapters on Gödel's famous incompleteness theorem, along with related results. The present volume begins with a bit more on propositional and first-order logic, followed by what I would call a "fein" chapter, which simultaneously generalizes some results from recursion theory, first-order arithmetic systems, and what I dub a "decision machine." Then come five chapters on formal systems, recursion theory and metamathematical applications in a general setting. The concluding five chapters are on the beautiful subject of combinatory logic, which is not only intriguing in its own right, but has important applications to computer science. Argonne National Laboratory is especially involved in these applications, and I am proud to say that its members have found use for some of my results in combinatory logic. This book does not cover such important subjects as set theory, model theory, proof theory, and modern developments in recursion theory, but the reader, after studying this volume, will be amply prepared for the study of these more advanced topics. Request Inspection Copy

Author : Raymond M. Smullyan
Publisher : Courier Corporation
Page : 292 pages
File Size : 51,6 Mb
Release : 2014-07-23
Category : Mathematics
ISBN : 9780486492377

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A Beginner's Guide to Mathematical Logic by Raymond M. Smullyan Pdf

Written by a creative master of mathematical logic, this introductory text combines stories of great philosophers, quotations, and riddles with the fundamentals of mathematical logic. Author Raymond Smullyan offers clear, incremental presentations of difficult logic concepts. He highlights each subject with inventive explanations and unique problems. Smullyan's accessible narrative provides memorable examples of concepts related to proofs, propositional logic and first-order logic, incompleteness theorems, and incompleteness proofs. Additional topics include undecidability, combinatoric logic, and recursion theory. Suitable for undergraduate and graduate courses, this book will also amuse and enlighten mathematically minded readers. Dover (2014) original publication. See every Dover book in print at www.doverpublications.com

Author : Raymond M. Smullyan
Publisher : Unknown
Page : 288 pages
File Size : 45,9 Mb
Release : 2017
Category : Electronic
ISBN : 9814733008

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Beginner's Further Guide To Mathematical Logic, A. by Raymond M. Smullyan Pdf

Author : Richard E. Hodel
Publisher : Courier Corporation
Page : 514 pages
File Size : 40,5 Mb
Release : 2013-01-01
Category : Mathematics
ISBN : 9780486497853

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An Introduction to Mathematical Logic by Richard E. Hodel Pdf

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 : Howard DeLong
Publisher : Courier Corporation
Page : 322 pages
File Size : 40,8 Mb
Release : 2012-09-26
Category : Mathematics
ISBN : 9780486139159

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A Profile of Mathematical Logic by Howard DeLong Pdf

This introduction to mathematical logic explores philosophical issues and Gödel's Theorem. Its widespread influence extends to the author of Gödel, Escher, Bach, whose Pulitzer Prize–winning book was inspired by this work.

Author : Joseph Mileti
Publisher : Cambridge University Press
Page : 518 pages
File Size : 47,5 Mb
Release : 2022-08-31
Category : Mathematics
ISBN : 9781108968195

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Modern Mathematical Logic by Joseph Mileti Pdf

This textbook gives a complete and modern introduction to mathematical logic. The author uses contemporary notation, conventions, and perspectives throughout, and emphasizes interactions with the rest of mathematics. In addition to covering the basic concepts of mathematical logic and the fundamental material on completeness, compactness, and incompleteness, it devotes significant space to thorough introductions to the pillars of the modern subject: model theory, set theory, and computability. Requiring only a modest background of undergraduate mathematics, the text can be readily adapted for a variety of one- or two-semester courses at the upper-undergraduate or beginning-graduate level. Numerous examples reinforce the key ideas and illustrate their applications, and a wealth of classroom-tested exercises serve to consolidate readers' understanding. Comprehensive and engaging, this book offers a fresh approach to this enduringly fascinating and important subject.

Author : P. D. Magnus,Tim Button,Robert Trueman,Richard Zach
Publisher : Unknown
Page : 0 pages
File Size : 42,9 Mb
Release : 2023
Category : Logic
ISBN : OCLC:1410964102

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Forall X by P. D. Magnus,Tim Button,Robert Trueman,Richard Zach Pdf

Author : W.D. Wallis
Publisher : Springer Science & Business Media
Page : 376 pages
File Size : 52,7 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475738261

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A Beginner’s Guide to Discrete Mathematics by W.D. Wallis Pdf

This introduction to discrete mathematics is aimed at freshmen and sophomores in mathematics and computer science. It begins with a survey of number systems and elementary set theory before moving on to treat data structures, counting, probability, relations and functions, graph theory, matrices, number theory and cryptography. The end of each section contains problem sets with selected solutions, and good examples occur throughout the text.

Author : Paolo Mancosu,Sergio Galvan,Richard Zach
Publisher : Oxford University Press
Page : 431 pages
File Size : 45,8 Mb
Release : 2021
Category : Philosophy
ISBN : 9780192895936

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An Introduction to Proof Theory by Paolo Mancosu,Sergio Galvan,Richard Zach Pdf

An Introduction to Proof Theory provides an accessible introduction to the theory of proofs, with details of proofs worked out and examples and exercises to aid the reader's understanding. It also serves as a companion to reading the original pathbreaking articles by Gerhard Gentzen. The first half covers topics in structural proof theory, including the Gödel-Gentzen translation of classical into intuitionistic logic (and arithmetic), natural deduction and the normalization theorems (for both NJ and NK), the sequent calculus, including cut-elimination and mid-sequent theorems, and various applications of these results. The second half examines ordinal proof theory, specifically Gentzen's consistency proof for first-order Peano Arithmetic. The theory of ordinal notations and other elements of ordinal theory are developed from scratch, and no knowledge of set theory is presumed. The proof methods needed to establish proof-theoretic results, especially proof by induction, are introduced in stages throughout the text. Mancosu, Galvan, and Zach's introduction will provide a solid foundation for those looking to understand this central area of mathematical logic and the philosophy of mathematics.

Author : Herbert B. Enderton
Publisher : Elsevier
Page : 330 pages
File Size : 49,8 Mb
Release : 2001-01-23
Category : Computers
ISBN : 9780080496467

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A Mathematical Introduction to Logic by Herbert B. Enderton Pdf

A Mathematical Introduction to Logic

Author : Michael S. Schneider
Publisher : Harper Collins
Page : 523 pages
File Size : 41,5 Mb
Release : 2014-04-01
Category : Science
ISBN : 9780062043160

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A Beginner's Guide to Constructing the Universe by Michael S. Schneider Pdf

Discover how mathematical sequences abound in our natural world in this definitive exploration of the geography of the cosmos You need not be a philosopher or a botanist, and certainly not a mathematician, to enjoy the bounty of the world around us. But is there some sort of order, a pattern, to the things that we see in the sky, on the ground, at the beach? In A Beginner's Guide to Constructing the Universe, Michael Schneider, an education writer and computer consultant, combines science, philosophy, art, and common sense to reaffirm what the ancients observed: that a consistent language of geometric design underpins every level of the universe, from atoms to galaxies, cucumbers to cathedrals. Schneider also discusses numerical and geometric symbolism through the ages, and concepts such as periodic renewal and resonance. This book is an education in the world and everything we can't see within it. Contains numerous b&w photos and illustrations.

Author : Peter Smith
Publisher : Cambridge University Press
Page : 370 pages
File Size : 44,7 Mb
Release : 2003-11-06
Category : Mathematics
ISBN : 0521008042

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An Introduction to Formal Logic by Peter Smith Pdf

Formal logic provides us with a powerful set of techniques for criticizing some arguments and showing others to be valid. These techniques are relevant to all of us with an interest in being skilful and accurate reasoners. In this highly accessible book, Peter Smith presents a guide to the fundamental aims and basic elements of formal logic. He introduces the reader to the languages of propositional and predicate logic, and then develops formal systems for evaluating arguments translated into these languages, concentrating on the easily comprehensible 'tree' method. His discussion is richly illustrated with worked examples and exercises. A distinctive feature is that, alongside the formal work, there is illuminating philosophical commentary. This book will make an ideal text for a first logic course, and will provide a firm basis for further work in formal and philosophical logic.

Author : George Tourlakis
Publisher : John Wiley & Sons
Page : 314 pages
File Size : 46,6 Mb
Release : 2011-03-01
Category : Mathematics
ISBN : 9781118030691

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Mathematical Logic by George Tourlakis Pdf

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 : Yu.I. Manin
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 53,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475743852

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A Course in Mathematical Logic by Yu.I. Manin Pdf

1. This book is above all addressed to mathematicians. It is intended to be a textbook of mathematical logic on a sophisticated level, presenting the reader with several of the most significant discoveries of the last ten or fifteen years. These include: the independence of the continuum hypothe sis, the Diophantine nature of enumerable sets, the impossibility of finding an algorithmic solution for one or two old problems. All the necessary preliminary material, including predicate logic and the fundamentals of recursive function theory, is presented systematically and with complete proofs. We only assume that the reader is familiar with "naive" set theoretic arguments. In this book mathematical logic is presented both as a part of mathe matics and as the result of its self-perception. Thus, the substance of the book consists of difficult proofs of subtle theorems, and the spirit of the book consists of attempts to explain what these theorems say about the mathematical way of thought. Foundational problems are for the most part passed over in silence. Most likely, logic is capable of justifying mathematics to no greater extent than biology is capable of justifying life. 2. The first two chapters are devoted to predicate logic. The presenta tion here is fairly standard, except that semantics occupies a very domi nant position, truth is introduced before deducibility, and models of speech in formal languages precede the systematic study of syntax.

Author : Alfred Tarski
Publisher : Courier Corporation
Page : 272 pages
File Size : 43,7 Mb
Release : 2013-07-04
Category : Mathematics
ISBN : 9780486318899

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Introduction to Logic by Alfred Tarski Pdf

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.