Logical Number Theory I
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Logical Number Theory I
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Author : Craig Smorynski
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Logical Number Theory I written by Craig Smorynski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Number theory as studied by the logician is the subject matter of the book. This first volume can stand on its own as a somewhat unorthodox introduction to mathematical logic for undergraduates, dealing with the usual introductory material: recursion theory, first-order logic, completeness, incompleteness, and undecidability. In addition, its second chapter contains the most complete logical discussion of Diophantine Decision Problems available anywhere, taking the reader right up to the frontiers of research (yet remaining accessible to the undergraduate). The first and third chapters also offer greater depth and breadth in logico-arithmetical matters than can be found in existing logic texts. Each chapter contains numerous exercises, historical and other comments aimed at developing the student's perspective on the subject, and a partially annotated bibliography.
Hilbert S Tenth Problem An Introduction To Logic Number Theory And Computability
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Author : M. Ram Murty
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-05-09
Hilbert S Tenth Problem An Introduction To Logic Number Theory And Computability written by M. Ram Murty and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-09 with Mathematics categories.
Hilbert's tenth problem is one of 23 problems proposed by David Hilbert in 1900 at the International Congress of Mathematicians in Paris. These problems gave focus for the exponential development of mathematical thought over the following century. The tenth problem asked for a general algorithm to determine if a given Diophantine equation has a solution in integers. It was finally resolved in a series of papers written by Julia Robinson, Martin Davis, Hilary Putnam, and finally Yuri Matiyasevich in 1970. They showed that no such algorithm exists. This book is an exposition of this remarkable achievement. Often, the solution to a famous problem involves formidable background. Surprisingly, the solution of Hilbert's tenth problem does not. What is needed is only some elementary number theory and rudimentary logic. In this book, the authors present the complete proof along with the romantic history that goes with it. Along the way, the reader is introduced to Cantor's transfinite numbers, axiomatic set theory, Turing machines, and Gödel's incompleteness theorems. Copious exercises are included at the end of each chapter to guide the student gently on this ascent. For the advanced student, the final chapter highlights recent developments and suggests future directions. The book is suitable for undergraduates and graduate students. It is essentially self-contained.
Mathematical Logic
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Author : H.-D. Ebbinghaus
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-11-15
Mathematical Logic written by H.-D. Ebbinghaus and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-11-15 with Mathematics categories.
This introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines. It covers several advanced topics not commonly treated in introductory texts, such as Fraïssé's characterization of elementary equivalence, Lindström's theorem on the maximality of first-order logic, and the fundamentals of logic programming.
Set Theory And Logic
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Author : Robert R. Stoll
language : en
Publisher: Courier Corporation
Release Date : 2012-05-23
Set Theory And Logic written by Robert R. Stoll and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-23 with Mathematics categories.
Explores sets and relations, the natural number sequence and its generalization, extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean algebras, informal axiomatic set theory, several algebraic theories, and 1st-order theories.
Elements Of Logic Via Numbers And Sets
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Author : D.L. Johnson
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-09-25
Elements Of Logic Via Numbers And Sets written by D.L. Johnson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-09-25 with Mathematics categories.
In mathematics we are interested in why a particular formula is true. Intuition and statistical evidence are insufficient, so we need to construct a formal logical proof. The purpose of this book is to describe why such proofs are important, what they are made of, how to recognize valid ones, how to distinguish different kinds, and how to construct them. This book is written for 1st year students with no previous experience of formulating proofs. Dave Johnson has drawn from his considerable experience to provide a text that concentrates on the most important elements of the subject using clear, simple explanations that require no background knowledge of logic. It gives many useful examples and problems, many with fully-worked solutions at the end of the book. In addition to a comprehensive index, there is also a useful `Dramatis Personae` an index to the many symbols introduced in the text, most of which will be new to students and which will be used throughout their degree programme.
Quintessence
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Author : Willard Van Orman Quine
language : en
Publisher: Harvard University Press
Release Date : 2008-04-30
Quintessence written by Willard Van Orman Quine and has been published by Harvard University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-30 with Philosophy categories.
Through the first half of the twentieth century, analytic philosophy was dominated by Russell, Wittgenstein, and Carnap. Influenced by Russell and especially by Carnap, another towering figure, Willard Van Orman Quine (1908Ð2000) emerged as the most important proponent of analytic philosophy during the second half of the century. Yet with twenty-three books and countless articles to his creditÑincluding, most famously, Word and Object and "Two Dogmas of Empiricism"ÑQuine remained a philosopher's philosopher, largely unknown to the general public. Quintessence for the first time collects Quine's classic essays (such as "Two Dogmas" and "On What There Is") in one volumeÑand thus offers readers a much-needed introduction to his general philosophy. Divided into six parts, the thirty-five selections take up analyticity and reductionism; the indeterminacy of translation of theoretical sentences and the inscrutability of reference; ontology; naturalized epistemology; philosophy of mind; and extensionalism. Representative of Quine at his best, these readings are fundamental not only to an appreciation of the philosopher and his work, but also to an understanding of the philosophical tradition that he so materially advanced.
A Logical Foundation For Potentialist Set Theory
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Author : Sharon Berry
language : en
Publisher: Cambridge University Press
Release Date : 2022-02-17
A Logical Foundation For Potentialist Set Theory written by Sharon Berry and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-17 with Mathematics categories.
A new approach to the standard axioms of set theory, relating the theory to the philosophy of science and metametaphysics.
Logic S Lost Genius
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Author : Eckart Menzler-Trott
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-05-05
Logic S Lost Genius written by Eckart Menzler-Trott and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-05 with Mathematics categories.
Gerhard Gentzen (1909–1945) is the founder of modern structural proof theory. His lasting methods, rules, and structures resulted not only in the technical mathematical discipline called “proof theory” but also in verification programs that are essential in computer science. The appearance, clarity, and elegance of Gentzen's work on natural deduction, the sequent calculus, and ordinal proof theory continue to be impressive even today. The present book gives the first comprehensive, detailed, accurate scientific biography expounding the life and work of Gerhard Gentzen, one of our greatest logicians, until his arrest and death in Prague in 1945. Particular emphasis in the book is put on the conditions of scientific research, in this case mathematical logic, in National Socialist Germany, the ideological fight for “German logic”, and their mutual protagonists. Numerous hitherto unpublished sources, family documents, archival material, interviews, and letters, as well as Gentzen's lectures for the mathematical public, make this book an indispensable source of information on this important mathematician, his work, and his time. The volume is completed by two deep substantial essays by Jan von Plato and Craig Smoryński on Gentzen's proof theory; its relation to the ideas of Hilbert, Brouwer, Weyl, and Gödel; and its development up to the present day. Smoryński explains the Hilbert program in more than the usual slogan form and shows why consistency is important. Von Plato shows in detail the benefits of Gentzen's program. This important book is a self-contained starting point for any work on Gentzen and his logic. The book is accessible to a wide audience with different backgrounds and is suitable for general readers, researchers, students, and teachers.
Introduction To Mathematical Logic Fourth Edition
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Author : Elliott Mendelson
language : en
Publisher: CRC Press
Release Date : 1997-06-01
Introduction To Mathematical Logic Fourth Edition written by Elliott Mendelson and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-06-01 with Mathematics categories.
The Fourth Edition of this long-established text retains all the key features of the previous editions, covering the basic topics of a solid first course in mathematical logic. This edition includes an extensive appendix on second-order logic, a section on set theory with urlements, and a section on the logic that results when we allow models with empty domains. The text contains numerous exercises and an appendix furnishes answers to many of them. Introduction to Mathematical Logic includes: propositional logic first-order logic first-order number theory and the incompleteness and undecidability theorems of Gödel, Rosser, Church, and Tarski axiomatic set theory theory of computability The study of mathematical logic, axiomatic set theory, and computability theory provides an understanding of the fundamental assumptions and proof techniques that form basis of mathematics. Logic and computability theory have also become indispensable tools in theoretical computer science, including artificial intelligence. Introduction to Mathematical Logic covers these topics in a clear, reader-friendly style that will be valued by anyone working in computer science as well as lecturers and researchers in mathematics, philosophy, and related fields.
Popular Lectures On Mathematical Logic
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Author : Hao Wang
language : en
Publisher: Courier Corporation
Release Date : 2014-09-22
Popular Lectures On Mathematical Logic written by Hao Wang and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-22 with Mathematics categories.
Noted logician discusses both theoretical underpinnings and practical applications, exploring set theory, model theory, recursion theory and constructivism, proof theory, logic's relation to computer science, and other subjects. 1981 edition, reissued by Dover in 1993 with a new Postscript by the author.