The Elements Of Mathematical Logic
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Mathematical Logic
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Author : J.D. Monk
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mathematical Logic written by J.D. Monk 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.
From the Introduction: "We shall base our discussion on a set-theoretical foundation like that used in developing analysis, or algebra, or topology. We may consider our task as that of giving a mathematical analysis of the basic concepts of logic and mathematics themselves. Thus we treat mathematical and logical practice as given empirical data and attempt to develop a purely mathematical theory of logic abstracted from these data." 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.
Elements Of Mathematical Logic
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Author : Georg Kreisel
language : en
Publisher:
Release Date : 1967
Elements Of Mathematical Logic written by Georg Kreisel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Logic, Symbolic and mathematical categories.
Mathematical Logic
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Author : Wei Li
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-02-26
Mathematical Logic written by Wei Li 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 2010-02-26 with Mathematics categories.
Mathematical logic is a branch of mathematics that takes axiom systems and mathematical proofs as its objects of study. This book shows how it can also provide a foundation for the development of information science and technology. The first five chapters systematically present the core topics of classical mathematical logic, including the syntax and models of first-order languages, formal inference systems, computability and representability, and Gödel’s theorems. The last five chapters present extensions and developments of classical mathematical logic, particularly the concepts of version sequences of formal theories and their limits, the system of revision calculus, proschemes (formal descriptions of proof methods and strategies) and their properties, and the theory of inductive inference. All of these themes contribute to a formal theory of axiomatization and its application to the process of developing information technology and scientific theories. The book also describes the paradigm of three kinds of language environments for theories and it presents the basic properties required of a meta-language environment. Finally, the book brings these themes together by describing a workflow for scientific research in the information era in which formal methods, interactive software and human invention are all used to their advantage. This book represents a valuable reference for graduate and undergraduate students and researchers in mathematics, information science and technology, and other relevant areas of natural sciences. Its first five chapters serve as an undergraduate text in mathematical logic and the last five chapters are addressed to graduate students in relevant disciplines.
Elements Of Mathematical Logic And Set Theory
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Author : Jerzy Słupecki
language : en
Publisher: Pergamon
Release Date : 1967
Elements Of Mathematical Logic And Set Theory written by Jerzy Słupecki and has been published by Pergamon this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Mathematics categories.
Mathematical Logic And Model Theory
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Author : Alexander Prestel
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-08-21
Mathematical Logic And Model Theory written by Alexander Prestel 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 2011-08-21 with Mathematics categories.
Mathematical Logic and Model Theory: A Brief Introduction offers a streamlined yet easy-to-read introduction to mathematical logic and basic model theory. It presents, in a self-contained manner, the essential aspects of model theory needed to understand model theoretic algebra. As a profound application of model theory in algebra, the last part of this book develops a complete proof of Ax and Kochen's work on Artin's conjecture about Diophantine properties of p-adic number fields. The character of model theoretic constructions and results differ quite significantly from that commonly found in algebra, by the treatment of formulae as mathematical objects. It is therefore indispensable to first become familiar with the problems and methods of mathematical logic. Therefore, the text is divided into three parts: an introduction into mathematical logic (Chapter 1), model theory (Chapters 2 and 3), and the model theoretic treatment of several algebraic theories (Chapter 4). This book will be of interest to both advanced undergraduate and graduate students studying model theory and its applications to algebra. It may also be used for self-study.
Modern Mathematical Logic
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Author : Joseph Mileti
language : en
Publisher: Cambridge University Press
Release Date : 2022-09-22
Modern Mathematical Logic written by Joseph Mileti 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 2022-09-22 with Mathematics categories.
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.
The Elements Of Mathematical Logic
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Author : Paul C. Rosenbloom
language : en
Publisher:
Release Date : 1950
The Elements Of Mathematical Logic written by Paul C. Rosenbloom and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1950 with Logic, Symbolic and mathematical categories.
"This book is intended for readers who, while mature mathematically, have no knowledge of mathematical logic. We attempt to introduce the reader to the most important approaches to the subject, and, wherever possible within the limitations of space which we have set for ourselves, to give at least a few nontrivial results illustrating each of the important methods for attacking logical problems"--Preface.
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.
The Elements Of Formal Logic
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Author : G. E. Hughes
language : en
Publisher: Routledge
Release Date : 2019-11-04
The Elements Of Formal Logic written by G. E. Hughes and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-04 with Philosophy categories.
Originally published in 1965. This is a textbook of modern deductive logic, designed for beginners but leading further into the heart of the subject than most other books of the kind. The fields covered are the Propositional Calculus, the more elementary parts of the Predicate Calculus, and Syllogistic Logic treated from a modern point of view. In each of the systems discussed the main emphases are on Decision Procedures and Axiomatisation, and the material is presented with as much formal rigour as is compatible with clarity of exposition. The techniques used are not only described but given a theoretical justification. Proofs of Consistency, Completeness and Independence are set out in detail. The fundamental characteristics of the various systems studies, and their relations to each other are established by meta-logical proofs, which are used freely in all sections of the book. Exercises are appended to most of the chapters, and answers are provided.
Introduction To Mathematical Logic Extended Edition
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Author : Michal Walicki
language : en
Publisher: World Scientific Publishing Company
Release Date : 2016-08-12
Introduction To Mathematical Logic Extended Edition written by Michal Walicki and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-12 with Mathematics categories.
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.