# constructivism in mathematics vol 2 studies in logic and the foundations of mathematics

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## Constructivism In Mathematics

**Author :**A.S. Troelstra

**ISBN :**9780080570884

**Genre :**Mathematics

**File Size :**30. 5 MB

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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.

## Philosophy Of Mathematics

**Author :**

**ISBN :**0080930581

**Genre :**Philosophy

**File Size :**50. 54 MB

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One of the most striking features of mathematics is the fact that we are much more certain about the mathematical knowledge we have than about what mathematical knowledge is knowledge of. Are numbers, sets, functions and groups physical entities of some kind? Are they objectively existing objects in some non-physical, mathematical realm? Are they ideas that are present only in the mind? Or do mathematical truths not involve referents of any kind? It is these kinds of questions that have encouraged philosophers and mathematicians alike to focus their attention on issues in the philosophy of mathematics. Over the centuries a number of reasonably well-defined positions about the nature of mathematics have been developed and it is these positions (both historical and current) that are surveyed in the current volume. Traditional theories (Platonism, Aristotelianism, Kantianism), as well as dominant modern theories (logicism, formalism, constructivism, fictionalism, etc.), are all analyzed and evaluated. Leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) is also discussed. The result is a handbook that not only provides a comprehensive overview of recent developments but that also serves as an indispensable resource for anyone wanting to learn about current developments in the philosophy of mathematics. -Comprehensive coverage of all main theories in the philosophy of mathematics -Clearly written expositions of fundamental ideas and concepts -Definitive discussions by leading researchers in the field -Summaries of leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) are also included

## Constructivism In Mathematics

**Author :**Anne Sjerp Troelstra

**ISBN :**0444703586

**Genre :**Mathematics

**File Size :**21. 6 MB

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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.

## Logical Approaches To Computational Barriers

**Author :**Arnold Beckmann

**ISBN :**9783540354666

**Genre :**Computers

**File Size :**48. 88 MB

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This book constitutes the refereed proceedings of the Second International Conference on Computability in Europe, CiE 2006, held in Swansea, UK, in June/July 2006. The 31 revised full papers presented together with 30 invited papers were carefully reviewed and selected from about 80 submissions. Among them are papers corresponding to 8 plenary talks and papers of 6 special sessions entitled proofs and computation, computable analysis, challenges in complexity, foundations of programming, mathematical models of computers and hypercomputers, and G??del centenary: G??del's legacy for computability.

## Logical Foundations Of Computer Science

**Author :**Sergei Artemov

**ISBN :**9783540926870

**Genre :**Computers

**File Size :**44. 48 MB

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This book constitutes the refereed proceedings of the International Symposium on Logical Foundations of Computer Science, LFCS 2009, held in Deerfield Beach, Florida, USA in January 2008. The volume presents 31 revised refereed papers carefully selected by the program committee. All current aspects of logic in computer science are addressed, including constructive mathematics and type theory, logical foundations of programming, logical aspects of computational complexity, logic programming and constraints, automated deduction and interactive theorem proving, logical methods in protocol and program verification and in program specification and extraction, domain theory logics, logical foundations of database theory, equational logic and term rewriting, lambda and combinatory calculi, categorical logic and topological semantics, linear logic, epistemic and temporal logics, intelligent and multiple agent system logics, logics of proof and justification, nonmonotonic reasoning, logic in game theory and social software, logic of hybrid systems, distributed system logics, system design logics, as well as other logics in computer science.

## Logic Mathematics Philosophy Vintage Enthusiasms

**Author :**David DeVidi

**ISBN :**9400702140

**Genre :**Philosophy

**File Size :**55. 14 MB

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The volume includes twenty-five research papers presented as gifts to John L. Bell to celebrate his 60th birthday by colleagues, former students, friends and admirers. Like Bellâ€™s own work, the contributions cross boundaries into several inter-related fields. The contributions are new work by highly respected figures, several of whom are among the key figures in their fields. Some examples: in foundations of maths and logic (William Lawvere, Peter Aczel, Graham Priest, Giovanni Sambin); analytical philosophy (Michael Dummett, William Demopoulos), philosophy of science (Michael Redhead, Frank Arntzenius), philosophy of mathematics (Michael Hallett, John Mayberry, Daniel Isaacson) and decision theory and foundations of economics (Ken Bimore). Most articles are contributions to current philosophical debates, but contributions also include some new mathematical results, important historical surveys, and a translation by Wilfrid Hodges of a key work of arabic logic.

## Mathematical Reviews

**Author :**

**ISBN :**UVA:X006122618

**Genre :**Mathematics

**File Size :**29. 53 MB

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## Computational Aspects Of Lie Group Representations And Related Topics

**Author :**Arjeh M. Cohen

**ISBN :**UCAL:B4405582

**Genre :**Lie groups

**File Size :**39. 46 MB

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## Constructive Kripke Semantics And Realizability

**Author :**James Lipton

**ISBN :**CORNELL:31924059480073

**Genre :**

**File Size :**41. 19 MB

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## Subject Guide To Books In Print

**Author :**

**ISBN :**STANFORD:36105025888517

**Genre :**American literature

**File Size :**50. 62 MB

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