Books in Mathematical logic and foundations

Constructivism in Mathematics, Vol 1

1st Edition
Volume 121
July 1, 1988
A.S. Troelstra + 1 more
English
Hardback
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eBook
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These two volumes cover the principal approaches to constructivism in mathematics. They present a thorough, up-to-date introduction to the metamathematics of constructive mathematics, paying special attention to Intuitionism, Markov's constructivism and Martin-Lof's type theory with its operational semantics. A detailed exposition of the basic features of constructive mathematics, with illustrations from analysis, algebra and topology, is provided, with due attention to the metamathematical aspects. Volume 1 is a self-contained introduction to the practice and foundations of constructivism, and does not require specialized knowledge beyond basic mathematical logic. Volume 2 contains mainly advanced topics of a proof-theoretical and semantical nature.

Logic Colloquium '86

1st Edition
Volume 124
November 1, 1987
F.R. Drake + 1 more
English

The result of the European Summer Meeting of the Association for Symbolic Logic, this volume gives an overview of the latest developments in most of the major fields of logic being actively pursued today. Important new developments in the applications of logic in computer science are presented. Other areas examined include model theory, set theory, recursion theory, proof theory, and the history of logic.This volume contains the texts of ten of the invited lectures and six of the contributed papers.

Logic Colloquium '85

1st Edition
Volume 122
January 1, 1987
The Paris Logic The Paris Logic Group
English
eBook
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The bulk of this volume consists of invited addresses presented at the Colloquium. These contributions report on recent or ongoing research in some of the mainstream areas of mathematical logic: model theory, both pure and in its applications (to group theory and real algebraic geometry); and proof theory, applied to set theory and diophantine equations.The major novel aspect of the book is the important place accorded to the connections of mathematical logic with the neighboring disciplines: mathematical foundations of computer science, and philosophy of mathematics.

Boole's Logic and Probability

2nd Edition
Volume 85
October 1, 1986
T. Hailperin
English
eBook
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Since the publication of the first edition in 1976, there has been a notable increase of interest in the development of logic. This is evidenced by the several conferences on the history of logic, by a journal devoted to the subject, and by an accumulation of new results. This increased activity and the new results - the chief one being that Boole's work in probability is best viewed as a probability logic - were influential circumstances conducive to a new edition.Chapter 1, presenting Boole's ideas on a mathematical treatment of logic, from their emergence in his early 1847 work on through to his immediate successors, has been considerably enlarged. Chapter 2 includes additional discussion of the ``uninterpretable'' notion, both semantically and syntactically. Chapter 3 now includes a revival of Boole's abandoned propositional logic and, also, a discussion of his hitherto unnoticed brush with ancient formal logic. Chapter 5 has an improved explanation of why Boole's probability method works. Chapter 6, Applications and Probability Logic, is a new addition. Changes from the first edition have brought about a three-fold increase in the bibliography.

Logic, Methodology and Philosophy of Science VII

1st Edition
Volume 114
May 1, 1986
R. Barcan Marcus + 2 more
English
eBook
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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
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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
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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
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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
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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/classic... context.

Handbook of Mathematical Logic

1st Edition
Volume 90
March 1, 1982
J. Barwise
English
eBook
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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.

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