An Algebraic Introduction To Mathematical Logic

Author : D.W. Barnes,J.M. Mack
Publisher : Springer Science & Business Media
Page : 129 pages
File Size : 53,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475744897

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An Algebraic Introduction to Mathematical Logic by D.W. Barnes,J.M. Mack Pdf

This book is intended for mathematicians. Its origins lie in a course of lectures given by an algebraist to a class which had just completed a substantial course on abstract algebra. Consequently, our treatment of the subject is algebraic. Although we assume a reasonable level of sophistication in algebra, the text requires little more than the basic notions of group, ring, module, etc. A more detailed knowledge of algebra is required for some of the exercises. We also assume a familiarity with the main ideas of set theory, including cardinal numbers and Zorn's Lemma. In this book, we carry out a mathematical study of the logic used in mathematics. We do this by constructing a mathematical model of logic and applying mathematics to analyse the properties of the model. We therefore regard all our existing knowledge of mathematics as being applicable to the analysis of the model, and in particular we accept set theory as part of the meta-Ianguage. We are not attempting to construct a foundation on which all mathematics is to be based--rather, any conclusions to be drawn about the foundations of mathematics come only by analogy with the model, and are to be regarded in much the same way as the conclusions drawn from any scientific theory.

Author : Donald Barnes,J.M. Mack
Publisher : Springer
Page : 123 pages
File Size : 40,6 Mb
Release : 2013-02-26
Category : Mathematics
ISBN : 1475744919

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An Algebraic Introduction to Mathematical Logic by Donald Barnes,J.M. Mack Pdf

This book is intended for mathematicians. Its origins lie in a course of lectures given by an algebraist to a class which had just completed a sub stantial course on abstract algebra. Consequently, our treatment ofthe sub ject is algebraic. Although we assurne a reasonable level of sophistication in algebra, the text requires little more than the basic notions of group, ring, module, etc. A more detailed knowledge of algebra is required for some of . the exercises. We also assurne a familiarity with the main ideas of set theory, including cardinal numbers and Zorn's Lemma. In this book, we carry out a mathematical study of the logic used in mathematics. We do this by constructing a mathematical model oflogic and applying mathematics to analyse the properties of the model. We therefore regard all our existing knowledge of mathematics as being applicable to the analysis of the model, and in particular we accept set theory as part of the meta-Ianguage. We are not attempting to construct a foundation on which all mathematics is to be based-rather, any conclusions to be drawn about the foundations of mathematics co me only by analogy with the model, and are to be regarded in much the same way as the conclusions drawn from any scientific theory.

Author : Donald W. Barnes,John M. Mack
Publisher : Unknown
Page : 121 pages
File Size : 40,7 Mb
Release : 1975
Category : Algebraic logic
ISBN : 3540901094

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An Algebraic Introduction to Mathematical Logic by Donald W. Barnes,John M. Mack Pdf

Author : Elliot Mendelsohn
Publisher : Springer Science & Business Media
Page : 351 pages
File Size : 53,6 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.

Author : Paul R. Halmos
Publisher : Courier Dover Publications
Page : 272 pages
File Size : 45,5 Mb
Release : 2016-03-17
Category : Mathematics
ISBN : 9780486810416

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Algebraic Logic by Paul R. Halmos Pdf

Beginning with an introduction to the concepts of algebraic logic, this concise volume features ten articles by a prominent mathematician that originally appeared in journals from 1954 to 1959. Covering monadic and polyadic algebras, these articles are essentially self-contained and accessible to a general mathematical audience, requiring no specialized knowledge of algebra or logic. Part One addresses monadic algebras, with articles on general theory, representation, and freedom. Part Two explores polyadic algebras, progressing from general theory and terms to equality. Part Three offers three items on polyadic Boolean algebras, including a survey of predicates, terms, operations, and equality. The book concludes with an additional bibliography and index.

Author : Elliott Mendelson
Publisher : Van Nostrand Reinhold Company
Page : 344 pages
File Size : 44,9 Mb
Release : 1979
Category : Mathematics
ISBN : UOM:39015039000214

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Introduction to Mathematical Logic by Elliott Mendelson Pdf

Author : Wolfgang Rautenberg
Publisher : Springer
Page : 337 pages
File Size : 46,9 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.

Author : Alexander Prestel,Charles N. Delzell
Publisher : Springer Science & Business Media
Page : 194 pages
File Size : 47,9 Mb
Release : 2011-08-21
Category : Mathematics
ISBN : 9781447121763

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Mathematical Logic and Model Theory by Alexander Prestel,Charles N. Delzell Pdf

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.

Author : Ladislav Rieger
Publisher : Elsevier
Page : 210 pages
File Size : 55,8 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483270524

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Algebraic Methods of Mathematical Logic by Ladislav Rieger Pdf

Algebraic Methods of Mathematical Logic focuses on the algebraic methods of mathematical logic, including Boolean algebra, mathematical language, and arithmetization. The book first offers information on the dialectic of the relation between mathematical and metamathematical aspects; metamathematico-mathematical parallelism and its natural limits; practical applications of methods of mathematical logic; and principal mathematical tools of mathematical logic. The text then elaborates on the language of mathematics and its symbolization and recursive construction of the relation of consequence. Discussions focus on recursive construction of the relation of consequence, fundamental descriptively-semantic rules, mathematical logic and mathematical language as a material system of signs, and the substance and purpose of symbolization of mathematical language. The publication examines expressive possibilities of symbolization; intuitive and mathematical notions of an idealized axiomatic mathematical theory; and the algebraic theory of elementary predicate logic. Topics include the notion of Boolean algebra based on joins, meets, and complementation, logical frame of a language and mathematical theory, and arithmetization and algebraization. The manuscript is a valuable reference for mathematicians and researchers interested in the algebraic methods of mathematical logic.

Author : Flora Dinkines
Publisher : Unknown
Page : 138 pages
File Size : 41,9 Mb
Release : 1964
Category : Algebra
ISBN : UOM:39015043411142

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Introduction to Mathematical Logic by Flora Dinkines Pdf

Author : Christopher C. Leary,Lars Kristiansen
Publisher : Lulu.com
Page : 382 pages
File Size : 48,8 Mb
Release : 2015
Category : Education
ISBN : 9781942341079

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A Friendly Introduction to Mathematical Logic by Christopher C. Leary,Lars Kristiansen Pdf

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 : Semen Grigorʹevich Gindikin
Publisher : Springer Science & Business Media
Page : 386 pages
File Size : 54,5 Mb
Release : 1985-10-14
Category : Mathematics
ISBN : 0387961798

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Algebraic Logic by Semen Grigorʹevich Gindikin Pdf

The popular literature on mathematical logic is rather extensive and written for the most varied categories of readers. College students or adults who read it in their free time may find here a vast number of thought-provoking logical problems. The reader who wishes to enrich his mathematical background in the hope that this will help him in his everyday life can discover detailed descriptions of practical (and quite often -- not so practical!) applications of logic. The large number of popular books on logic has given rise to the hope that by applying mathematical logic, students will finally learn how to distinguish between necessary and sufficient conditions and other points of logic in the college course in mathematics. But the habit of teachers of mathematical analysis, for example, to stick to problems dealing with sequences without limit, uniformly continuous functions, etc. has, unfortunately, led to the writing of textbooks that present prescriptions for the mechanical construction of definitions of negative concepts which seem to obviate the need for any thinking on the reader's part. We are most certainly not able to enumerate everything the reader may draw out of existing books on mathematical logic, however.

Author : Aldo Ursini
Publisher : Routledge
Page : 584 pages
File Size : 43,6 Mb
Release : 2017-10-05
Category : Mathematics
ISBN : 9781351434713

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Logic and Algebra by Aldo Ursini Pdf

""Attempts to unite the fields of mathematical logic and general algebra. Presents a collection of refereed papers inspired by the International Conference on Logic and Algebra held in Siena, Italy, in honor of the late Italian mathematician Roberto Magari, a leading force in the blossoming of research in mathematical logic in Italy since the 1960s.

Author : Shashi Mohan Srivastava
Publisher : Springer Science & Business Media
Page : 198 pages
File Size : 45,8 Mb
Release : 2013-01-16
Category : Mathematics
ISBN : 9781461457466

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A Course on Mathematical Logic by Shashi Mohan Srivastava Pdf

This is a short, modern, and motivated introduction to mathematical logic for upper undergraduate and beginning graduate students in mathematics and computer science. Any mathematician who is interested in getting acquainted with logic and would like to learn Gödel’s incompleteness theorems should find this book particularly useful. The treatment is thoroughly mathematical and prepares students to branch out in several areas of mathematics related to foundations and computability, such as logic, axiomatic set theory, model theory, recursion theory, and computability. In this new edition, many small and large changes have been made throughout the text. The main purpose of this new edition is to provide a healthy first introduction to model theory, which is a very important branch of logic. Topics in the new chapter include ultraproduct of models, elimination of quantifiers, types, applications of types to model theory, and applications to algebra, number theory and geometry. Some proofs, such as the proof of the very important completeness theorem, have been completely rewritten in a more clear and concise manner. The new edition also introduces new topics, such as the notion of elementary class of structures, elementary diagrams, partial elementary maps, homogeneous structures, definability, and many more.

Author : H.-D. Ebbinghaus,J. Flum,Wolfgang Thomas
Publisher : Springer Science & Business Media
Page : 290 pages
File Size : 53,6 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.