Iterated Inductive Definitions And Subsystems Of Analysis Recent Proof Theoretical Studies
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Iterated Inductive Definitions And Subsystems Of Analysis Recent Proof Theoretical Studies
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Author : W. Buchholz
language : en
Publisher: Springer
Release Date : 2006-11-14
Iterated Inductive Definitions And Subsystems Of Analysis Recent Proof Theoretical Studies written by W. Buchholz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Iterated Inductive Definitions And Subsystems Of Analysis
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Author : W. Buchholz
language : en
Publisher:
Release Date : 2014-01-15
Iterated Inductive Definitions And Subsystems Of Analysis written by W. Buchholz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Iterated Inductive Definitions And Subsystems Of Analysis
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Author : Wilfried Buchholz
language : en
Publisher: Springer Verlag
Release Date : 1981-01-01
Iterated Inductive Definitions And Subsystems Of Analysis written by Wilfried Buchholz and has been published by Springer Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981-01-01 with Mathematics categories.
Iterated Inductive Definitions And Subsystems Of Analysis
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Author :
language : en
Publisher:
Release Date : 1982
Iterated Inductive Definitions And Subsystems Of Analysis written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with categories.
Feferman On Foundations
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Author : Gerhard Jäger
language : en
Publisher: Springer
Release Date : 2018-04-04
Feferman On Foundations written by Gerhard Jäger and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-04 with Mathematics categories.
This volume honours the life and work of Solomon Feferman, one of the most prominent mathematical logicians of the latter half of the 20th century. In the collection of essays presented here, researchers examine Feferman’s work on mathematical as well as specific methodological and philosophical issues that tie into mathematics. Feferman’s work was largely based in mathematical logic (namely model theory, set theory, proof theory and computability theory), but also branched out into methodological and philosophical issues, making it well known beyond the borders of the mathematics community. With regard to methodological issues, Feferman supported concrete projects. On the one hand, these projects calibrate the proof theoretic strength of subsystems of analysis and set theory and provide ways of overcoming the limitations imposed by Gödel’s incompleteness theorems through appropriate conceptual expansions. On the other, they seek to identify novel axiomatic foundations for mathematical practice, truth theories, and category theory. In his philosophical research, Feferman explored questions such as “What is logic?” and proposed particular positions regarding the foundations of mathematics including, for example, his “conceptual structuralism.” The contributing authors of the volume examine all of the above issues. Their papers are accompanied by an autobiography presented by Feferman that reflects on the evolution and intellectual contexts of his work. The contributing authors critically examine Feferman’s work and, in part, actively expand on his concrete mathematical projects. The volume illuminates Feferman’s distinctive work and, in the process, provides an enlightening perspective on the foundations of mathematics and logic.
Proof Theory
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Author : Peter Aczel
language : en
Publisher: Cambridge University Press
Release Date : 1992
Proof Theory written by Peter Aczel 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 1992 with Computers categories.
The lecture courses in this work are derived from the SERC 'Logic for IT' Summer School and Conference on Proof Theory held at Leeds University. The contributions come from acknowledged experts and comprise expository and research articles; put together in this book they form an invaluable introduction to proof theory that is aimed at both mathematicians and computer scientists.
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.
Mathesis Universalis Computability And Proof
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Author : Stefania Centrone
language : en
Publisher: Springer Nature
Release Date : 2019-10-25
Mathesis Universalis Computability And Proof written by Stefania Centrone and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-25 with Philosophy categories.
In a fragment entitled Elementa Nova Matheseos Universalis (1683?) Leibniz writes “the mathesis [...] shall deliver the method through which things that are conceivable can be exactly determined”; in another fragment he takes the mathesis to be “the science of all things that are conceivable.” Leibniz considers all mathematical disciplines as branches of the mathesis and conceives the mathesis as a general science of forms applicable not only to magnitudes but to every object that exists in our imagination, i.e. that is possible at least in principle. As a general science of forms the mathesis investigates possible relations between “arbitrary objects” (“objets quelconques”). It is an abstract theory of combinations and relations among objects whatsoever. In 1810 the mathematician and philosopher Bernard Bolzano published a booklet entitled Contributions to a Better-Grounded Presentation of Mathematics. There is, according to him, a certain objective connection among the truths that are germane to a certain homogeneous field of objects: some truths are the “reasons” (“Gründe”) of others, and the latter are “consequences” (“Folgen”) of the former. The reason-consequence relation seems to be the counterpart of causality at the level of a relation between true propositions. Arigorous proof is characterized in this context as a proof that shows the reason of the proposition that is to be proven. Requirements imposed on rigorous proofs seem to anticipate normalization results in current proof theory. The contributors of Mathesis Universalis, Computability and Proof, leading experts in the fields of computer science, mathematics, logic and philosophy, show the evolution of these and related ideas exploring topics in proof theory, computability theory, intuitionistic logic, constructivism and reverse mathematics, delving deeply into a contextual examination of the relationship between mathematical rigor and demands for simplification.
Ordinal Analysis With An Introduction To Proof Theory
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Author : Toshiyasu Arai
language : en
Publisher: Springer Nature
Release Date : 2020-08-11
Ordinal Analysis With An Introduction To Proof Theory written by Toshiyasu Arai and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-11 with Philosophy categories.
This book provides readers with a guide to both ordinal analysis, and to proof theory. It mainly focuses on ordinal analysis, a research topic in proof theory that is concerned with the ordinal theoretic content of formal theories. However, the book also addresses ordinal analysis and basic materials in proof theory of first-order or omega logic, presenting some new results and new proofs of known ones.Primarily intended for graduate students and researchers in mathematics, especially in mathematical logic, the book also includes numerous exercises and answers for selected exercises, designed to help readers grasp and apply the main results and techniques discussed.
Concepts Of Proof In Mathematics Philosophy And Computer Science
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Author : Dieter Probst
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2016-07-25
Concepts Of Proof In Mathematics Philosophy And Computer Science written by Dieter Probst and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-25 with Philosophy categories.
A proof is a successful demonstration that a conclusion necessarily follows by logical reasoning from axioms which are considered evident for the given context and agreed upon by the community. It is this concept that sets mathematics apart from other disciplines and distinguishes it as the prototype of a deductive science. Proofs thus are utterly relevant for research, teaching and communication in mathematics and of particular interest for the philosophy of mathematics. In computer science, moreover, proofs have proved to be a rich source for already certified algorithms. This book provides the reader with a collection of articles covering relevant current research topics circled around the concept 'proof'. It tries to give due consideration to the depth and breadth of the subject by discussing its philosophical and methodological aspects, addressing foundational issues induced by Hilbert's Programme and the benefits of the arising formal notions of proof, without neglecting reasoning in natural language proofs and applications in computer science such as program extraction.