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9 produkter

Constructivism in Mathematics, Vol 1

AvD. van Dalen,A.S. Troelstra

E-bok

PDF, Engelska, 1988

783 kr

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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.

Constructivism in Mathematics, Vol 2

AvD. van Dalen,A.S. Troelstra

E-bok

PDF, Engelska, 2014

783 kr

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Studies in Logic and the Foundations of Mathematics, Volume 123: Constructivism in Mathematics: An Introduction, Vol. II focuses on various studies in mathematics and logic, including metric spaces, polynomial rings, and Heyting algebras.The publication first takes a look at the topology of metric spaces, algebra, and finite-type arithmetic and theories of operators. Discussions focus on intuitionistic finite-type arithmetic, theories of operators and classes, rings and modules, linear algebra, polynomial rings, fields and local rings, complete separable metric spaces, and located sets. The text then examines proof theory of intuitionistic logic, theory of types and constructive set theory, and choice sequences.The book elaborates on semantical completeness, sheaves, sites, and higher-order logic, and applications of sheaf models. Topics include a derived rule of local continuity, axiom of countable choice, forcing over sites, sheaf models for higher-order logic, and complete Heyting algebras.The publication is a valuable reference for mathematicians and researchers interested in mathematics and logic.

Logic Colloquium '80

AvD. Lascar,T.J. Smileym. fl.

E-bok

PDF, Engelska, 2009

238 kr

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The papers appearing in this volume are part of those originally intended for presentation at the conference: Logic Colloquium ''80 - European Summer Meeting of the Association for Symbolic Logic (A.S.L.) which was to takeplace in Prague, August 24·30, 1980, principally under the auspices of the Czech Academy of Sciences. There were 36 invited speakers from Western and Eastern Europe, Israel, the U.S., and the U.S.S.R. The local organizingcommittee cabled participants on July 15, 1980 to inform them that the meeting was cancelled for technical reasons; a subsequent communication stated that the cancellation was due to unforeseen circumstances lying beyond the controlof the organizing committee.The unexpected cancellation of the Prague meeting was greatly regretted, since so much care, time, and energy had been given to its advance preparation by the local organizing committee as well as by representatives of the A.S.L.and its European Committee. The late date on which cancellation took place required drastic changes of plans by speakers and participants. Last-minute efforts to reschedule the meeting elsewhere in Europe could not be realized.

Del 121 - Studies in Logic and the Foundations of Mathematics

Constructivism in Mathematics, Vol 1

AvA.S. Troelstra,D. van Dalen

Inbunden, Engelska, 1988

703 kr

Skickas inom 10-15 vardagar

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.

Del 123 - Studies in Logic and the Foundations of Mathematics

Constructivism in Mathematics, Vol 2

AvA.S. Troelstra,D. van Dalen

Inbunden, Engelska, 1988

798 kr

Skickas inom 10-15 vardagar

The publication first takes a look at the topology of metric spaces, algebra, and finite-type arithmetic and theories of operators. Discussions focus on intuitionistic finite-type arithmetic, theories of operators and classes, rings and modules, linear algebra, polynomial rings, fields and local rings, complete separable metric spaces, and located sets. The text then examines proof theory of intuitionistic logic, theory of types and constructive set theory, and choice sequences.

The book elaborates on semantical completeness, sheaves, sites, and higher-order logic, and applications of sheaf models. Topics include a derived rule of local continuity, axiom of countable choice, forcing over sites, sheaf models for higher-order logic, and complete Heyting algebras.

The publication is a valuable reference for mathematicians and researchers interested in mathematics and logic.

Brouwer's Cambridge Lectures on Intuitionism

AvLuitzen Egbertus Jan Brouwer,D. van Dalen

Häftad, Engelska, 2011

521 kr

Skickas inom 7-10 vardagar

Luitzen Egburtus Jan Brouwer founded a school of thought whose aim was to include mathematics within the framework of intuitionistic philosophy; mathematics was to be regarded as an essentially free development of the human mind. What emerged diverged considerably at some points from tradition, but intuitionism has survived well the struggle between contending schools in the foundations of mathematics and exact philosophy. Originally published in 1981, this monograph contains a series of lectures dealing with most of the fundamental topics such as choice sequences, the continuum, the fan theorem, order and well-order. Brouwer's own powerful style is evident throughout the work.

Sets: Naive, Axiomatic and Applied

A Basic Compendium with Exercises for Use in Set Theory for Non Logicians, Working and Teaching Mathematicians and Students

AvH. De Swart,H. C. Doetsm. fl.

E-bok

PDF, Engelska, 2014

783 kr

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Sets: Naïve, Axiomatic and Applied is a basic compendium on naïve, axiomatic, and applied set theory and covers topics ranging from Boolean operations to union, intersection, and relative complement as well as the reflection principle, measurable cardinals, and models of set theory. Applications of the axiom of choice are also discussed, along with infinite games and the axiom of determinateness. Comprised of three chapters, this volume begins with an overview of naïve set theory and some important sets and notations. The equality of sets, subsets, and ordered pairs are considered, together with equivalence relations and real numbers. The next chapter is devoted to axiomatic set theory and discusses the axiom of regularity, induction and recursion, and ordinal and cardinal numbers. In the final chapter, applications of set theory are reviewed, paying particular attention to filters, Boolean algebra, and inductive definitions together with trees and the Borel hierarchy. This book is intended for non-logicians, students, and working and teaching mathematicians.

Sets and integration An outline of the development

AvD. van Dalen

E-bok

PDF, Engelska, 2012

712 kr

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The present text resulted from lectures given by the authors at the Rijks Universiteit at Utrecht. These lectures were part of a series on ''History of Contemporary Mathematics''. The need for such an enterprise was generally felt, since the curriculum at many universities is designed to suit an efficient treatment of advanced subjects rather than to reflect the development of notions and techniques. As it is very likely that this trend will continue, we decided to offer lectures of a less technical nature to provide students and interested listeners with a survey of the history of topics in our present-day mathematics. We consider it very useful for a mathematician to have an acquaintance with the history of the development of his subject, especially in the nineteenth century where the germs of many of modern disciplines can be found. Our attention has therefore been mainly directed to relatively young developments. In the lectures we tried to stay clear of both oversimplification and extreme technicality. The result is a text, that should not cause difficulties to a reader with a working knowledge of mathematics. The developments sketched in this book are fundamental for many areas in mathematics and the notions considered are crucial almost everywhere. The book may be most useful, in particular, for those teaching mathematics.

Sets and integration An outline of the development

AvD. van Dalen

Häftad, Engelska, 2011

546 kr

Skickas inom 10-15 vardagar

The present text resulted from lectures given by the authors at the Rijks Universiteit at Utrecht. These lectures were part of a series on 'History of Contemporary Mathematics'. The need for such an enterprise was generally felt, since the curriculum at many universities is designed to suit an efficient treatment of advanced subjects rather than to reflect the development of notions and techniques. As it is very likely that this trend will continue, we decided to offer lectures of a less technical nature to provide students and interested listeners with a survey of the history of topics in our present-day mathematics. We consider it very useful for a mathematician to have an acquaintance with the history of the development of his subject, especially in the nineteenth century where the germs of many of modern disciplines can be found. Our attention has therefore been mainly directed to relatively young developments. In the lectures we tried to stay clear of both oversimplification and extreme technicality. The result is a text, that should not cause difficulties to a reader with a working knowledge of mathematics. The developments sketched in this book are fundamental for many areas in mathematics and the notions considered are crucial almost everywhere. The book may be most useful, in particular, for those teaching mathematics.

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D. van Dalen – författare

Constructivism in Mathematics, Vol 1

Constructivism in Mathematics, Vol 2

Logic Colloquium '80

Constructivism in Mathematics, Vol 1

Constructivism in Mathematics, Vol 2

Brouwer's Cambridge Lectures on Intuitionism

Sets: Naive, Axiomatic and Applied

Sets and integration An outline of the development

Sets and integration An outline of the development

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