Subsystems Of Second Order Arithmetic
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Subsystems Of Second Order Arithmetic
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Author : Stephen George Simpson
language : en
Publisher: Cambridge University Press
Release Date : 2009-05-29
Subsystems Of Second Order Arithmetic written by Stephen George Simpson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-29 with Mathematics categories.
This volume examines appropriate axioms for mathematics to prove particular theorems in core areas.
Subsystems Of Second Order Arithmetic
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Author : Stephen George Simpson
language : en
Publisher:
Release Date : 2014-05-14
Subsystems Of Second Order Arithmetic written by Stephen George Simpson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with Mathematics categories.
Through a series of case studies, this volume examines these axioms to prove particular theorems in core mathematical areas.
Subsystems Of Second Order Arithmetic
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Author : Stephen G. Simpson
language : en
Publisher: Springer
Release Date : 2012-01-28
Subsystems Of Second Order Arithmetic written by Stephen G. Simpson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-28 with Mathematics categories.
An original contribution to the foundations of mathematics, with emphasis on the role of set existence axioms, this book gives particular attention to several well known foundational programs including those by Hilbert, Bishop, and Weyl. The book includes an extensive bibliography and a detailed index, and should become a long-term standard reference in its field.
Reverse Mathematics
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Author : John Stillwell
language : en
Publisher: Princeton University Press
Release Date : 2019-09-24
Reverse Mathematics written by John Stillwell and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-24 with Mathematics categories.
This volume presents reverse mathematics to a general mathematical audience for the first time. Stillwell gives a representative view of this field, emphasizing basic analysis--finding the "right axioms" to prove fundamental theorems--and giving a novel approach to logic. to logic.
Handbook Of Proof Theory
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Author : S.R. Buss
language : en
Publisher: Elsevier
Release Date : 1998-07-09
Handbook Of Proof Theory written by S.R. Buss and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-07-09 with Mathematics categories.
This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth.The chapters are arranged so that the two introductory articles come first; these are then followed by articles from core classical areas of proof theory; the handbook concludes with articles that deal with topics closely related to computer science.
Logic And Theory Of Algorithms
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Author : Arnold Beckmann
language : en
Publisher: Springer
Release Date : 2008-06-11
Logic And Theory Of Algorithms written by Arnold Beckmann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-11 with Computers categories.
CiE 2008: Logic and Theory of Algorithms Athens, Greece, June 15–20, 2008 Computability in Europe (CiE) is an informal network of European scientists working on computability theory, including its foundations, technical devel- ment, and applications. Among the aims of the network is to advance our t- oretical understanding of what can and cannot be computed, by any means of computation. Its scienti?c vision is broad: computations may be performed with discrete or continuous data by all kinds of algorithms, programs, and - chines. Computations may be made by experimenting with any sort of physical system obeying the laws of a physical theory such as Newtonian mechanics, quantum theory, or relativity. Computations may be very general, depending on the foundations of set theory; or very speci?c, using the combinatorics of ?nite structures. CiE also works on subjects intimately related to computation, especially theories of data and information, and methods for formal reasoning about computations. The sources of new ideas and methods include practical developments in areas such as neural networks, quantum computation, natural computation, molecular computation, computational learning. Applications are everywhere,especially, in algebra,analysisand geometry, or data types and p- gramming. Within CiE there is general recognition of the underlying relevance of computability to physics and a broad range of other sciences, providing as it does a basic analysis of the causal structure of dynamical systems. Thisvolume,Logic andTheory of Algorithms,istheproceedingsofthefourth in a series of conferences of CiE that was held at the University of Athens, June 15–20, 2008.
Logicism Intuitionism And Formalism
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Author : Sten Lindström
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-11-25
Logicism Intuitionism And Formalism written by Sten Lindström 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 2008-11-25 with Mathematics categories.
This anthology reviews the programmes in the foundations of mathematics from the classical period and assesses their possible relevance for contemporary philosophy of mathematics. A special section is concerned with constructive mathematics.
Hilbert S Programs And Beyond
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Author : Wilfried Sieg
language : en
Publisher: Oxford University Press
Release Date : 2013-03-07
Hilbert S Programs And Beyond written by Wilfried Sieg 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 2013-03-07 with Computers categories.
David Hilbert was one of the great mathematicians who expounded the centrality of their subject in human thought. In this collection of essays, Wilfried Sieg frames Hilbert's foundational work, from 1890 to 1939, in a comprehensive way and integrates it with modern proof theoretic investigations.
Mathematical Logic And Computation
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Author : Jeremy Avigad
language : en
Publisher:
Release Date : 2022-11-09
Mathematical Logic And Computation written by Jeremy Avigad and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-09 with Computers categories.
This new book on mathematical logic by Jeremy Avigad gives a thorough introduction to the fundamental results and methods of the subject from the syntactic point of view, emphasizing logic as the study of formal languages and systems and their proper use. Topics include proof theory, model theory, the theory of computability, and axiomatic foundations, with special emphasis given to aspects of mathematical logic that are fundamental to computer science, including deductive systems, constructive logic, the simply typed lambda calculus, and type-theoretic foundations. Clear and engaging, with plentiful examples and exercises, it is an excellent introduction to the subject for graduate students and advanced undergraduates who are interested in logic in mathematics, computer science, and philosophy, and an invaluable reference for any practicing logician's bookshelf.
Kurt G Del
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Author : Solomon Feferman
language : en
Publisher: Cambridge University Press
Release Date : 2010-04-19
Kurt G Del written by Solomon Feferman and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-19 with Mathematics categories.
Kurt Gödel (1906–1978) did groundbreaking work that transformed logic and other important aspects of our understanding of mathematics, especially his proof of the incompleteness of formalized arithmetic. This book on different aspects of his work and on subjects in which his ideas have contemporary resonance includes papers from a May 2006 symposium celebrating Gödel's centennial as well as papers from a 2004 symposium. Proof theory, set theory, philosophy of mathematics, and the editing of Gödel's writings are among the topics covered. Several chapters discuss his intellectual development and his relation to predecessors and contemporaries such as Hilbert, Carnap, and Herbrand. Others consider his views on justification in set theory in light of more recent work and contemporary echoes of his incompleteness theorems and the concept of constructible sets.