An Outline Of Mathematical Logic

Author : A. Grzegorczyk
Publisher : Springer Science & Business Media
Page : 604 pages
File Size : 48,5 Mb
Release : 2013-03-07
Category : Philosophy
ISBN : 9789401022040

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An Outline of Mathematical Logic by A. Grzegorczyk Pdf

Recent years have seen the appearance of many English-Ianguage hand books of logie and numerous monographs on topieal discoveries in the foundations of mathematies. These publications on the foundations of mathematies as a whole are rather difficult for the beginners or refer the reader to other handbooks and various pieeemeal eontribu tions and also sometimes to largely conceived "mathematical fol klore" of unpublished results. As distinct from these, the present book is as easy as possible systematic exposition of the now classical results in the foundations of mathematics. Henee the book may be useful especially for those readers who want to have all the proofs carried out in full and all the concepts explained in detail. In this sense the book is self-contained. The reader's ability to guess is not assumed, and the author's ambition was to reduce the use of sueh words as evident and obvious in proofs to aminimum. This is why the book, it is believed, may be helpful in teaehing or learning the foundation of mathematics in those situations in which the student cannot refer to a parallel lecture on the subject. This is also the reason that I do not insert in the book the last results and the most modem and fashionable approaches to the subjeet, which does not enrich the essential knowledge in founda tions but ean discourage the beginner by their abstract form. A. G.

Author : A. Grzegorczyk
Publisher : Unknown
Page : 608 pages
File Size : 41,5 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 9401022054

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An Outline of Mathematical Logic by A. Grzegorczyk Pdf

Author : Joseph R. Shoenfield
Publisher : CRC Press
Page : 281 pages
File Size : 42,6 Mb
Release : 2018-05-02
Category : Mathematics
ISBN : 9781351433303

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Mathematical Logic by Joseph R. Shoenfield Pdf

This classic introduction to the main areas of mathematical logic provides the basis for a first graduate course in the subject. It embodies the viewpoint that mathematical logic is not a collection of vaguely related results, but a coherent method of attacking some of the most interesting problems, which face the mathematician. The author presents the basic concepts in an unusually clear and accessible fashion, concentrating on what he views as the central topics of mathematical logic: proof theory, model theory, recursion theory, axiomatic number theory, and set theory. There are many exercises, and they provide the outline of what amounts to a second book that goes into all topics in more depth. This book has played a role in the education of many mature and accomplished researchers.

Author : Andrzej Grzegorczyk
Publisher : Springer
Page : 606 pages
File Size : 51,6 Mb
Release : 2011-12-10
Category : Philosophy
ISBN : 9401021139

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An Outline of Mathematical Logic by Andrzej Grzegorczyk Pdf

Recent years have seen the appearance of many English-language hand books of logic and numerous monographs on topical discoveries in the foundations of mathematics. These publications on the foundations of mathematics as a whole are rather difficult for the beginners or refer the reader to other handbooks and various piecemeal contribu tions and also sometimes to largely conceived "mathematical fol klore" of unpublished results. As distinct from these, the present book is as easy as possible systematic exposition of the now classical results in the foundations of mathematics. Hence the book may be useful especially for those readers who want to have all the proofs carried out in full and all the concepts explained in detail. In this sense the book is self-contained. The reader's ability to guess is not assumed, and the author's ambition was to reduce the use of such words as evident and obvious in proofs to a minimum. This is why the book, it is believed, may be helpful in teaching or learning the foundation of mathematics in those situations in which the student cannot refer to a parallel lecture on the subject. This is also the reason that I do not insert in the book the last results and the most modem and fashionable approaches to the subject, which does not enrich the essential knowledge in founda tions but can discourage the beginner by their abstract form. A. G.

Author : Angelo Margaris
Publisher : Courier Corporation
Page : 244 pages
File Size : 44,5 Mb
Release : 1990-01-01
Category : Mathematics
ISBN : 0486662691

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First Order Mathematical Logic by Angelo Margaris Pdf

"Attractive and well-written introduction." — Journal of Symbolic Logic The logic that mathematicians use to prove their theorems is itself a part of mathematics, in the same way that algebra, analysis, and geometry are parts of mathematics. This attractive and well-written introduction to mathematical logic is aimed primarily at undergraduates with some background in college-level mathematics; however, little or no acquaintance with abstract mathematics is needed. Divided into three chapters, the book begins with a brief encounter of naïve set theory and logic for the beginner, and proceeds to set forth in elementary and intuitive form the themes developed formally and in detail later. In Chapter Two, the predicate calculus is developed as a formal axiomatic theory. The statement calculus, presented as a part of the predicate calculus, is treated in detail from the axiom schemes through the deduction theorem to the completeness theorem. Then the full predicate calculus is taken up again, and a smooth-running technique for proving theorem schemes is developed and exploited. Chapter Three is devoted to first-order theories, i.e., mathematical theories for which the predicate calculus serves as a base. Axioms and short developments are given for number theory and a few algebraic theories. Then the metamathematical notions of consistency, completeness, independence, categoricity, and decidability are discussed, The predicate calculus is proved to be complete. The book concludes with an outline of Godel's incompleteness theorem. Ideal for a one-semester course, this concise text offers more detail and mathematically relevant examples than those available in elementary books on logic. Carefully chosen exercises, with selected answers, help students test their grasp of the material. For any student of mathematics, logic, or the interrelationship of the two, this book represents a thought-provoking introduction to the logical underpinnings of mathematical theory. "An excellent text." — Mathematical Reviews

Author : J. N. Crossley,C.J. Ash,C.J. Brickhill,J.C. Stillwell
Publisher : Courier Corporation
Page : 96 pages
File Size : 51,7 Mb
Release : 2012-08-29
Category : Mathematics
ISBN : 9780486151526

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What Is Mathematical Logic? by J. N. Crossley,C.J. Ash,C.J. Brickhill,J.C. Stillwell Pdf

A serious introductory treatment geared toward non-logicians, this survey traces the development of mathematical logic from ancient to modern times and discusses the work of Planck, Einstein, Bohr, Pauli, Heisenberg, Dirac, and others. 1972 edition.

Author : J. Barwise
Publisher : Elsevier
Page : 1164 pages
File Size : 51,8 Mb
Release : 1982-03-01
Category : Computers
ISBN : 9780080933641

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Handbook of Mathematical Logic by J. Barwise Pdf

The handbook is divided into four parts: model theory, set theory, recursion theory and proof theory. Each of the four parts begins with a short guide to the chapters that follow. Each chapter is written for non-specialists in the field in question. Mathematicians will find that this book provides them with a unique opportunity to apprise themselves of developments in areas other than their own.

Author : Heinz-Dieter Ebbinghaus,Jörg Flum,Wolfgang Thomas
Publisher : Springer Nature
Page : 304 pages
File Size : 41,8 Mb
Release : 2021-05-28
Category : Mathematics
ISBN : 9783030738396

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Mathematical Logic by Heinz-Dieter Ebbinghaus,Jörg 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.

Author : Alonzo Church
Publisher : Princeton University Press
Page : 392 pages
File Size : 54,9 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400881451

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Introduction to Mathematical Logic (PMS-13), Volume 13 by Alonzo Church Pdf

Logic is sometimes called the foundation of mathematics: the logician studies the kinds of reasoning used in the individual steps of a proof. Alonzo Church was a pioneer in the field of mathematical logic, whose contributions to number theory and the theories of algorithms and computability laid the theoretical foundations of computer science. His first Princeton book, The Calculi of Lambda-Conversion (1941), established an invaluable tool that computer scientists still use today. Even beyond the accomplishment of that book, however, his second Princeton book, Introduction to Mathematical Logic, defined its subject for a generation. Originally published in Princeton's Annals of Mathematics Studies series, this book was revised in 1956 and reprinted a third time, in 1996, in the Princeton Landmarks in Mathematics series. Although new results in mathematical logic have been developed and other textbooks have been published, it remains, sixty years later, a basic source for understanding formal logic. Church was one of the principal founders of the Association for Symbolic Logic; he founded the Journal of Symbolic Logic in 1936 and remained an editor until 1979 At his death in 1995, Church was still regarded as the greatest mathematical logician in the world.

Author : Joel W. Robbin
Publisher : Courier Dover Publications
Page : 239 pages
File Size : 42,9 Mb
Release : 2006-07-07
Category : Mathematics
ISBN : 9780486450186

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Mathematical Logic by Joel W. Robbin Pdf

This self-contained text will appeal to readers from diverse fields and varying backgrounds. Topics include 1st-order recursive arithmetic, 1st- and 2nd-order logic, and the arithmetization of syntax. Numerous exercises; some solutions. 1969 edition.

Author : Richard L. Epstein
Publisher : Princeton University Press
Page : 545 pages
File Size : 41,9 Mb
Release : 2006-07-23
Category : Mathematics
ISBN : 9780691123004

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Classical Mathematical Logic by Richard L. Epstein Pdf

In Classical Mathematical Logic, Richard L. Epstein relates the systems of mathematical logic to their original motivations to formalize reasoning in mathematics. The book also shows how mathematical logic can be used to formalize particular systems of mathematics. It sets out the formalization not only of arithmetic, but also of group theory, field theory, and linear orderings. These lead to the formalization of the real numbers and Euclidean plane geometry. The scope and limitations of modern logic are made clear in these formalizations. The book provides detailed explanations of all proofs and the insights behind the proofs, as well as detailed and nontrivial examples and problems. The book has more than 550 exercises. It can be used in advanced undergraduate or graduate courses and for self-study and reference. Classical Mathematical Logic presents a unified treatment of material that until now has been available only by consulting many different books and research articles, written with various notation systems and axiomatizations.

Author : Raymond M. Smullyan
Publisher : Courier Corporation
Page : 292 pages
File Size : 55,8 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 : Joseph Mileti
Publisher : Cambridge University Press
Page : 517 pages
File Size : 49,7 Mb
Release : 2022-09-22
Category : Mathematics
ISBN : 9781108833141

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Modern Mathematical Logic by Joseph Mileti Pdf

This textbook gives a comprehensive and modern introduction to mathematical logic at the upper-undergraduate and beginning graduate level.

Author : Peter G. Hinman
Publisher : CRC Press
Page : 894 pages
File Size : 43,7 Mb
Release : 2018-10-08
Category : Mathematics
ISBN : 9781439864272

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Fundamentals of Mathematical Logic by Peter G. Hinman Pdf

This introductory graduate text covers modern mathematical logic from propositional, first-order and infinitary logic and Gödel's Incompleteness Theorems to extensive introductions to set theory, model theory and recursion (computability) theory. Based on the author's more than 35 years of teaching experience, the book develops students' intuition by presenting complex ideas in the simplest context for which they make sense. The book is appropriate for use as a classroom text, for self-study, and as a reference on the state of modern logic.

Author : Stephen Cole Kleene
Publisher : Courier Corporation
Page : 416 pages
File Size : 52,9 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.