Logic Of Mathematics

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Logic of Mathematics

Zofia Adamowicz,Pawel Zbierski
Logic of Mathematics Book PDF

Author : Zofia Adamowicz,Pawel Zbierski
Publisher : John Wiley & Sons
Page : 276 pages
File Size : 41,5 Mb
Release : 2011-09-26
Category : Mathematics
ISBN : 9781118030790

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Logic of Mathematics by Zofia Adamowicz,Pawel Zbierski Pdf

A thorough, accessible, and rigorous presentation of the central theorems of mathematical logic . . . ideal for advanced students of mathematics, computer science, and logic Logic of Mathematics combines a full-scale introductory course in mathematical logic and model theory with a range of specially selected, more advanced theorems. Using a strict mathematical approach, this is the only book available that contains complete and precise proofs of all of these important theorems: * Gödel's theorems of completeness and incompleteness * The independence of Goodstein's theorem from Peano arithmetic * Tarski's theorem on real closed fields * Matiyasevich's theorem on diophantine formulas Logic of Mathematics also features: * Full coverage of model theoretical topics such as definability, compactness, ultraproducts, realization, and omission of types * Clear, concise explanations of all key concepts, from Boolean algebras to Skolem-Löwenheim constructions and other topics * Carefully chosen exercises for each chapter, plus helpful solution hints At last, here is a refreshingly clear, concise, and mathematically rigorous presentation of the basic concepts of mathematical logic-requiring only a standard familiarity with abstract algebra. Employing a strict mathematical approach that emphasizes relational structures over logical language, this carefully organized text is divided into two parts, which explain the essentials of the subject in specific and straightforward terms. Part I contains a thorough introduction to mathematical logic and model theory-including a full discussion of terms, formulas, and other fundamentals, plus detailed coverage of relational structures and Boolean algebras, Gödel's completeness theorem, models of Peano arithmetic, and much more. Part II focuses on a number of advanced theorems that are central to the field, such as Gödel's first and second theorems of incompleteness, the independence proof of Goodstein's theorem from Peano arithmetic, Tarski's theorem on real closed fields, and others. No other text contains complete and precise proofs of all of these theorems. With a solid and comprehensive program of exercises and selected solution hints, Logic of Mathematics is ideal for classroom use-the perfect textbook for advanced students of mathematics, computer science, and logic.

Mathematical Logic

H.-D. Ebbinghaus,J. Flum,Wolfgang Thomas
Mathematical Logic Book PDF

Author : H.-D. Ebbinghaus,J. Flum,Wolfgang Thomas
Publisher : Springer Science & Business Media
Page : 290 pages
File Size : 52,6 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475723557

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Mathematical Logic by H.-D. Ebbinghaus,J. Flum,Wolfgang Thomas Pdf

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.

Math-a-Logic

Dianne Draze
Math a Logic Book PDF

Author : Dianne Draze
Publisher : Taylor & Francis
Page : 84 pages
File Size : 43,6 Mb
Release : 2021-09-03
Category : Education
ISBN : 9781000501513

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Math-a-Logic by Dianne Draze Pdf

If you thought math was all numbers, you're in for a surprise. The ability to reason logically is both a prerequisite for learning mathematics and a desired outcome of mathematics instruction. Mathematics provides an excellent context in which to make students aware of the logical structures they need to function successfully in any setting. Math-A-Logic is an award-winning text that successfully merges logical thinking with mathematical concepts and calculations. Eight areas of logic are introduced: patterns and sequences, analogies, deduction, inference, sets and Venn diagram, propositions and logical notation, syllogisms, and logical problem solving. Attractive, reproducible worksheets lead students through each topic, providing explanations, examples, and exercises to test their understanding. With mathematics as the vehicle for presenting and practicing the logical concept, students get practice in mathematical concepts and computations while building thinking skills. The end result is clearer thinking and enhanced problem-solving abilities. This unique approach is sure to be a favorite supplement to your regular math program. The attractive illustrations, clear instructions, solid content, and ease of use make this book a winner. This book is the winner of Learning Magazine's Teacher Choice award. Grades 4-8

Introduction to Mathematical Logic

Elliot Mendelsohn
Introduction to Mathematical Logic Book PDF

Author : Elliot Mendelsohn
Publisher : Springer Science & Business Media
Page : 351 pages
File Size : 50,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461572886

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Introduction to Mathematical Logic by Elliot Mendelsohn Pdf

This is a compact mtroduction to some of the pnncipal tOpICS of mathematical logic . In the belief that beginners should be exposed to the most natural and easiest proofs, I have used free-swinging set-theoretic methods. The significance of a demand for constructive proofs can be evaluated only after a certain amount of experience with mathematical logic has been obtained. If we are to be expelled from "Cantor's paradise" (as nonconstructive set theory was called by Hilbert), at least we should know what we are missing. The major changes in this new edition are the following. (1) In Chapter 5, Effective Computability, Turing-computabIlity IS now the central notion, and diagrams (flow-charts) are used to construct Turing machines. There are also treatments of Markov algorithms, Herbrand-Godel-computability, register machines, and random access machines. Recursion theory is gone into a little more deeply, including the s-m-n theorem, the recursion theorem, and Rice's Theorem. (2) The proofs of the Incompleteness Theorems are now based upon the Diagonalization Lemma. Lob's Theorem and its connection with Godel's Second Theorem are also studied. (3) In Chapter 2, Quantification Theory, Henkin's proof of the completeness theorem has been postponed until the reader has gained more experience in proof techniques. The exposition of the proof itself has been improved by breaking it down into smaller pieces and using the notion of a scapegoat theory. There is also an entirely new section on semantic trees.

Mathematics and Logic

Mark Kac,Stanislaw M. Ulam
Mathematics and Logic Book PDF

Author : Mark Kac,Stanislaw M. Ulam
Publisher : Courier Corporation
Page : 189 pages
File Size : 53,6 Mb
Release : 1992-01-01
Category : Philosophy
ISBN : 9780486670850

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Mathematics and Logic by Mark Kac,Stanislaw M. Ulam Pdf

Fascinating study of the origin and nature of mathematical thought, including relation of mathematics and science, 20th-century developments, impact of computers, and more.Includes 34 illustrations. 1968 edition."

A Concise Introduction to Mathematical Logic

Wolfgang Rautenberg
A Concise Introduction to Mathematical Logic Book PDF

Author : Wolfgang Rautenberg
Publisher : Springer
Page : 337 pages
File Size : 52,5 Mb
Release : 2010-07-01
Category : Mathematics
ISBN : 9781441912213

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A Concise Introduction to Mathematical Logic by Wolfgang Rautenberg Pdf

Mathematical logic developed into a broad discipline with many applications in mathematics, informatics, linguistics and philosophy. This text introduces the fundamentals of this field, and this new edition has been thoroughly expanded and revised.

Mathematical Logic

Roman Kossak
Mathematical Logic Book PDF

Author : Roman Kossak
Publisher : Springer
Page : 186 pages
File Size : 53,5 Mb
Release : 2018-10-03
Category : Mathematics
ISBN : 9783319972985

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Mathematical Logic by Roman Kossak Pdf

This book, presented in two parts, offers a slow introduction to mathematical logic, and several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions. Its first part, Logic Sets, and Numbers, shows how mathematical logic is used to develop the number structures of classical mathematics. The exposition does not assume any prerequisites; it is rigorous, but as informal as possible. All necessary concepts are introduced exactly as they would be in a course in mathematical logic; but are accompanied by more extensive introductory remarks and examples to motivate formal developments. The second part, Relations, Structures, Geometry, introduces several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions, and shows how they are used to study and classify mathematical structures. Although more advanced, this second part is accessible to the reader who is either already familiar with basic mathematical logic, or has carefully read the first part of the book. Classical developments in model theory, including the Compactness Theorem and its uses, are discussed. Other topics include tameness, minimality, and order minimality of structures. The book can be used as an introduction to model theory, but unlike standard texts, it does not require familiarity with abstract algebra. This book will also be of interest to mathematicians who know the technical aspects of the subject, but are not familiar with its history and philosophical background.

The Elements of Mathematical Logic

Paul C. Rosenbloom
The Elements of Mathematical Logic Book PDF

Author : Paul C. Rosenbloom
Publisher : Courier Dover Publications
Page : 0 pages
File Size : 55,5 Mb
Release : 2005
Category : Logic, Symbolic and mathematical
ISBN : 0486446174

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The Elements of Mathematical Logic by Paul C. Rosenbloom Pdf

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.

A Course in Mathematical Logic

Yu.I. Manin
A Course in Mathematical Logic Book PDF

Author : Yu.I. Manin
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 42,6 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.

Logic for Mathematics and Computer Science

Stanley Burris
Logic for Mathematics and Computer Science Book PDF

Author : Stanley Burris
Publisher : Upper Saddle River, N.J. : Prentice Hall
Page : 456 pages
File Size : 51,8 Mb
Release : 1998
Category : Computers
ISBN : UOM:39015040561261

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Logic for Mathematics and Computer Science by Stanley Burris Pdf

This text is intended for one semester courses in Logic, it can also be applied to a two semester course, in either Computer Science or Mathematics Departments. Unlike other texts on mathematical logic that are either too advanced, too sparse in examples or exercises, too traditional in coverage, or too philosophical in approach, this text provides an elementary "hands-on" presentation of important mathematical logic topics, new and old, that is readily accessible and relevant to all students of the mathematical sciences -- not just those in traditional pure mathematics.

Mathematical Logic

George Tourlakis
Mathematical Logic Book PDF

Author : George Tourlakis
Publisher : John Wiley & Sons
Page : 314 pages
File Size : 47,9 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.

Mathematical Logic

Stephen Cole Kleene
Mathematical Logic Book PDF

Author : Stephen Cole Kleene
Publisher : Courier Corporation
Page : 416 pages
File Size : 43,8 Mb
Release : 2013-04-22
Category : Mathematics
ISBN : 9780486317076

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Mathematical Logic by Stephen Cole Kleene Pdf

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.

Foundations of Logic and Mathematics

Yves Nievergelt
Foundations of Logic and Mathematics Book PDF

Author : Yves Nievergelt
Publisher : Springer Science & Business Media
Page : 425 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461201250

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Foundations of Logic and Mathematics by Yves Nievergelt Pdf

This modern introduction to the foundations of logic and mathematics not only takes theory into account, but also treats in some detail applications that have a substantial impact on everyday life (loans and mortgages, bar codes, public-key cryptography). A first college-level introduction to logic, proofs, sets, number theory, and graph theory, and an excellent self-study reference and resource for instructors.

A Profile of Mathematical Logic

Howard DeLong
A Profile of Mathematical Logic Book PDF

Author : Howard DeLong
Publisher : Courier Corporation
Page : 322 pages
File Size : 45,7 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.

Sets, Logic and Maths for Computing

David Makinson
Sets Logic and Maths for Computing Book PDF

Author : David Makinson
Publisher : Springer Science & Business Media
Page : 283 pages
File Size : 55,7 Mb
Release : 2012-02-27
Category : Computers
ISBN : 9781447125006

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Sets, Logic and Maths for Computing by David Makinson Pdf

This easy-to-follow textbook introduces the mathematical language, knowledge and problem-solving skills that undergraduates need to study computing. The language is in part qualitative, with concepts such as set, relation, function and recursion/induction; but it is also partly quantitative, with principles of counting and finite probability. Entwined with both are the fundamental notions of logic and their use for representation and proof. Features: teaches finite math as a language for thinking, as much as knowledge and skills to be acquired; uses an intuitive approach with a focus on examples for all general concepts; brings out the interplay between the qualitative and the quantitative in all areas covered, particularly in the treatment of recursion and induction; balances carefully the abstract and concrete, principles and proofs, specific facts and general perspectives; includes highlight boxes that raise common queries and clear confusions; provides numerous exercises, with selected solutions.