Mathematical Logic And The Foundations Of Mathematics
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Mathematical Logic And The Foundations Of Mathematics
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Author : G. T. Kneebone
language : en
Publisher:
Release Date : 1963
Mathematical Logic And The Foundations Of Mathematics written by G. T. Kneebone and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Logic, Symbolic and mathematical categories.
Mathematical Logic And The Foundations Of Mathematics
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Author : G. T.. Kneebone
language : en
Publisher:
Release Date : 1926
Mathematical Logic And The Foundations Of Mathematics written by G. T.. Kneebone and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1926 with categories.
Mathematical Logic And The Foundations Of Mathematics
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Author : Geoffrey Thomas Kneebone
language : en
Publisher:
Release Date : 1953
Mathematical Logic And The Foundations Of Mathematics written by Geoffrey Thomas Kneebone and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1953 with categories.
Handbook Of Mathematical Logic
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Author : J. Barwise
language : en
Publisher: Elsevier
Release Date : 1982-03-01
Handbook Of Mathematical Logic written by J. Barwise and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-03-01 with Computers categories.
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.
Logic Foundations Of Mathematics And Computability Theory
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Author : Robert E. Butts
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Logic Foundations Of Mathematics And Computability Theory written by Robert E. Butts 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 Science categories.
The Fifth International Congress of Logic, Methodology and Philosophy of Science was held at the University of Western Ontario, London, Canada, 27 August to 2 September 1975. The Congress was held under the auspices of the International Union of History and Philosophy of Science, Division of Logic, Methodology and Philosophy of Science, and was sponsored by the National Research Council of Canada and the University of Western Ontario. As those associated closely with the work of the Division over the years know well, the work undertaken by its members varies greatly and spans a number of fields not always obviously related. In addition, the volume of work done by first rate scholars and scientists in the various fields of the Division has risen enormously. For these and related reasons it seemed to the editors chosen by the Divisional officers that the usual format of publishing the proceedings of the Congress be abandoned in favour of a somewhat more flexible, and hopefully acceptable, method of pre sentation. Accordingly, the work of the invited participants to the Congress has been divided into four volumes appearing in the University of Western Ontario Series in Philosophy of Science. The volumes are entitled, Logic, Foundations of Mathematics and Computability Theory, Foun dational Problems in the Special Sciences, Basic Problems in Methodol ogy and Linguistics, and Historical and Philosophical Dimensions of Logic, Methodology and Philosophy of Science.
The Logical Foundations Of Mathematics
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Author : William S. Hatcher
language : en
Publisher: Elsevier
Release Date : 2014-05-09
The Logical Foundations Of Mathematics written by William S. Hatcher and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-09 with Mathematics categories.
The Logical Foundations of Mathematics offers a study of the foundations of mathematics, stressing comparisons between and critical analyses of the major non-constructive foundational systems. The position of constructivism within the spectrum of foundational philosophies is discussed, along with the exact relationship between topos theory and set theory. Comprised of eight chapters, this book begins with an introduction to first-order logic. In particular, two complete systems of axioms and rules for the first-order predicate calculus are given, one for efficiency in proving metatheorems, and the other, in a "natural deduction" style, for presenting detailed formal proofs. A somewhat novel feature of this framework is a full semantic and syntactic treatment of variable-binding term operators as primitive symbols of logic. Subsequent chapters focus on the origin of modern foundational studies; Gottlob Frege's formal system intended to serve as a foundation for mathematics and its paradoxes; the theory of types; and the Zermelo-Fraenkel set theory. David Hilbert's program and Kurt Gödel's incompleteness theorems are also examined, along with the foundational systems of W. V. Quine and the relevance of categorical algebra for foundations. This monograph will be of interest to students, teachers, practitioners, and researchers in mathematics.
Mathematical Logic
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Author : Wei Li
language : en
Publisher: Springer
Release Date : 2014-11-07
Mathematical Logic written by Wei Li and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-07 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. The second edition of the book includes major revisions on the proof of the completeness theorem of the Gentzen system and new contents on the logic of scientific discovery, R-calculus without cut, and the operational semantics of program debugging. 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.
Mathematical Logic
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Author : Heinz-Dieter Ebbinghaus
language : en
Publisher: Springer Nature
Release Date : 2021-05-28
Mathematical Logic written by Heinz-Dieter Ebbinghaus and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-28 with Mathematics categories.
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.
The Adventure Of Reason
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Author : Paolo Mancosu
language : en
Publisher: Oxford University Press
Release Date : 2010-11-18
The Adventure Of Reason written by Paolo Mancosu and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-18 with Mathematics categories.
Paolo Mancosu presents an innovative set of studies of logic and the foundations of mathematics in the first half of the 20th century. He sheds new light on important topics such as the relationship between phenomenology and the exact sciences, the nature of truth and logical consequence, and the nature of mathematical intuition.
The Foundations Of Mathematics
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Author : Kenneth Kunen
language : en
Publisher:
Release Date : 2009
The Foundations Of Mathematics written by Kenneth Kunen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
Mathematical logic grew out of philosophical questions regarding the foundations of mathematics, but logic has now outgrown its philosophical roots, and has become an integral part of mathematics in general. This book is designed for students who plan to specialize in logic, as well as for those who are interested in the applications of logic to other areas of mathematics. Used as a text, it could form the basis of a beginning graduate-level course. There are three main chapters: Set Theory, Model Theory, and Recursion Theory. The Set Theory chapter describes the set-theoretic foundations of all of mathematics, based on the ZFC axioms. It also covers technical results about the Axiom of Choice, well-orderings, and the theory of uncountable cardinals. The Model Theory chapter discusses predicate logic and formal proofs, and covers the Completeness, Compactness, and Lowenheim-Skolem Theorems, elementary submodels, model completeness, and applications to algebra. This chapter also continues the foundational issues begun in the set theory chapter. Mathematics can now be viewed as formal proofs from ZFC. Also, model theory leads to models of set theory. This includes a discussion of absoluteness, and an analysis of models such as H( ) and R( ). The Recursion Theory chapter develops some basic facts about computable functions, and uses them to prove a number of results of foundational importance; in particular, Church's theorem on the undecidability of logical consequence, the incompleteness theorems of Godel, and Tarski's theorem on the non-definability of truth.