Books in Mathematical logic and foundations

131-140 of 141 results in All results

Logic, Methodology and Philosophy of Science VII

• 1st Edition
• Volume 114
• May 1, 1986
• R. Barcan Marcus + 2 more
• English
• eBook 978-0-08-096039-5

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Harvey Friedman's Research on the Foundations of Mathematics

• 1st Edition
• Volume 117
• November 1, 1985
• L.A. Harrington + 3 more
• English
• eBook 978-0-08-096040-1

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This volume discusses various aspects of Harvey Friedman's research in the foundations of mathematics over the past fifteen years. It should appeal to a wide audience of mathematicians, computer scientists, and mathematically oriented philosophers.

Equivalents of the Axiom of Choice, II

• 1st Edition
• Volume 116
• March 1, 1985
• H. Rubin + 1 more
• English
• eBook 978-0-08-088765-4

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This monograph contains a selection of over 250 propositions which are equivalent to AC. The first part on set forms has sections on the well-ordering theorem, variants of AC, the law of the trichotomy, maximal principles, statements related to the axiom of foundation, forms from algebra, cardinal number theory, and a final section of forms from topology, analysis and logic. The second part deals with the axiom of choice for classes - well-ordering theorem, choice and maximal principles.

Cylindric Algebras

• 1st Edition
• Volume 115
• February 1, 1985
• Bozzano G Luisa
• English
• eBook 978-0-08-088758-6

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Volume II completes the description of the main aspects of the theory, covering representation questions, model theory and decision problems for them, translations from logic to algebra and vice-versa, and relationships with other algebraic versions of logic.

Intensional Mathematics

• 1st Edition
• Volume 113
• January 1, 1985
• S. Shapiro
• English
• eBook 978-0-08-088004-4

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``Platonism and intuitionism are rival philosophies of Mathematics, the former holding that the subject matter of mathematics consists of abstract objects whose existence is independent of the mathematician, the latter that the subject matter consists of mental construction... both views are implicitly opposed to materialistic accounts of mathematics which take the subject matter of mathematics to consist (in a direct way) of material objects...'' FROM THE INTRODUCTIONAmong the aims of this book are: - The discussion of some important philosophical issues using the precision of mathematics. - The development of formal systems that contain both classical and constructive components. This allows the study of constructivity in otherwise classical contexts and represents the formalization of important intensional aspects of mathematical practice. - The direct formalization of intensional concepts (such as computability) in a mixed constructive/classical context.

The Lambda Calculus

• 2nd Edition
• Volume 103
• October 1, 1984
• H.P. Barendregt
• English
• eBook 978-0-08-093375-7

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The revised edition contains a new chapter which provides an elegant description of the semantics. The various classes of lambda calculus models are described in a uniform manner. Some didactical improvements have been made to this edition. An example of a simple model is given and then the general theory (of categorical models) is developed. Indications are given of those parts of the book which can be used to form a coherent course.

Handbook of Mathematical Logic

• 1st Edition
• Volume 90
• March 1, 1982
• J. Barwise
• English
• eBook 978-0-08-093364-1

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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, Methodology and Philosophy of Science VI

• 1st Edition
• January 1, 1982
• J.J. Cohen + 3 more
• English
• eBook 978-0-08-096030-2

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Logic, Methodology and Philosophy of Science VI presents the results of recent research into the foundations of science. The volume contains invited papers presented at the Congress, covering the areas of Logic, Mathematics, Physical Sciences, Biological Sciences and the Humanities.

Mathematical Logic in Computer Science

• 1st Edition
• January 1, 1981
• B. Dömölki + 1 more
• English
• Hardback 978-0-444-85440-7

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This volume contains 31 papers prepared for the Colloquium on Mathematical Logic in Programming held in Salgótarján, Hungary. Main topics of the Colloquium include:- Model theoretical, universal algebra and category theoretical approaches to program semantics- Logical and model theoretical approaches to program-verification, data representation and problem specification- Logical and model theoretical approaches to theorem proving, automatic programming and automatic problem solving- Very high level, logical based programming languages.

Introduction to Metamathematics

• 1st Edition
• January 1, 1980
• S.C. Kleene
• English
• Hardback 978-0-7204-2103-3

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Stephen Cole Kleene was one of the greatest logicians of the twentieth century and this book is the influential textbook he wrote to teach the subject to the next generation. It was first published in 1952, some twenty years after the publication of Gadel's paper on the incompleteness of arithmetic, which marked, if not the beginning of modern logic, at least a turning point after which nothing was ever the same. Kleene was an important figure in logic, and lived a long full life of scholarship and teaching. The 1930s was a time of creativity and ferment in the subject, when the notion of computable moved from the realm of philosophical speculation to the realm of science. This was accomplished by the work of Kurt Gade1, Alan Turing, and Alonzo Church, who gave three apparently different precise definitions of computable. When they all turned out to be equivalent, there was a collective realization that this was indeed the right notion. Kleene played a key role in this process. One could say that he was there at the beginning of modern logic. He showed the equivalence of lambda calculus with Turing machines and with Gadel's recursion equations, and developed the modern machinery of partial recursive functions. This textbook played an invaluable part in educating the logicians of the present. It played an important role in their own logical education.