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A Course On Mathematical Logic

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A Course In Mathematical Logic

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Author : I͡U. I. Manin
language : en
Publisher: Springer Science & Business Media
Release Date : 1977

A Course In Mathematical Logic written by I͡U. I. Manin 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 1977 with Mathematics categories.

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.

A Course In Mathematical Logic

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Author :
language : en
Publisher:
Release Date : 1977

A Course In Mathematical Logic written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Logic, Symbolic and mathematical categories.

A Course In Mathematical Logic

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Author : Yu.I. Manin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

A Course In Mathematical Logic written by Yu.I. Manin 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 2013-06-29 with Mathematics categories.

A Course On Mathematical Logic

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Author : Shashi Mohan Srivastava
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-01-16

A Course On Mathematical Logic written by Shashi Mohan Srivastava 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 2013-01-16 with Mathematics categories.

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.

A Course In Mathematical Logic For Mathematicians

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Author : Yu. I. Manin
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-10-13

A Course In Mathematical Logic For Mathematicians written by Yu. I. Manin 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 2009-10-13 with Mathematics categories.

1. The ?rst edition of this book was published in 1977. The text has been well received and is still used, although it has been out of print for some time. In the intervening three decades, a lot of interesting things have happened to mathematical logic: (i) Model theory has shown that insights acquired in the study of formal languages could be used fruitfully in solving old problems of conventional mathematics. (ii) Mathematics has been and is moving with growing acceleration from the set-theoretic language of structures to the language and intuition of (higher) categories, leaving behind old concerns about in?nities: a new view of foundations is now emerging. (iii) Computer science, a no-nonsense child of the abstract computability theory, has been creatively dealing with old challenges and providing new ones, such as the P/NP problem. Planning additional chapters for this second edition, I have decided to focus onmodeltheory,the conspicuousabsenceofwhichinthe ?rsteditionwasnoted in several reviews, and the theory of computation, including its categorical and quantum aspects. The whole Part IV: Model Theory, is new. I am very grateful to Boris I. Zilber, who kindly agreed to write it. It may be read directly after Chapter II. The contents of the ?rst edition are basically reproduced here as Chapters I–VIII. Section IV.7, on the cardinality of the continuum, is completed by Section IV.7.3, discussing H. Woodin’s discovery.

A Course In Mathematical Logic

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Author : J.L. Bell
language : en
Publisher: Elsevier
Release Date : 1977-01-01

A Course In Mathematical Logic written by J.L. Bell and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977-01-01 with Mathematics categories.

A comprehensive one-year graduate (or advanced undergraduate) course in mathematical logic and foundations of mathematics. No previous knowledge of logic is required; the book is suitable for self-study. Many exercises (with hints) are included.