Proof Theory Constructive Mathematics

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Proof Theory Constructive Mathematics

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Author : Dirk van Dalen
language : en
Publisher:
Release Date : 1987

Proof Theory Constructive Mathematics written by Dirk van Dalen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with categories.

Omega Bibliography Of Mathematical Logic Proof Theory Constructive Mathematics

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Author :
language : en
Publisher:
Release Date : 1987

Omega Bibliography Of Mathematical Logic Proof Theory Constructive Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Logic, Symbolic and mathematical categories.

Proof Theory

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Author : Wolfram Pohlers
language : en
Publisher: Springer
Release Date : 2009-06-10

Proof Theory written by Wolfram Pohlers and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-10 with Mathematics categories.

Although this is an introductory text on proof theory, most of its contents is not found in a unified form elsewhere in the literature, except at a very advanced level. The heart of the book is the ordinal analysis of axiom systems, with particular emphasis on that of the impredicative theory of elementary inductive definitions on the natural numbers. The "constructive" consequences of ordinal analysis are sketched out in the epilogue. The book provides a self-contained treatment assuming no prior knowledge of proof theory and almost none of logic. The author has, moreover, endeavoured not to use the "cabal language" of proof theory, but only a language familiar to most readers.

Foundations Of Constructive Probability Theory

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Author : Yuen-Kwok Chan
language : en
Publisher: Cambridge University Press
Release Date : 2021-05-27

Foundations Of Constructive Probability Theory written by Yuen-Kwok Chan 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 2021-05-27 with Mathematics categories.

Using Bishop's work on constructive analysis as a framework, this monograph gives a systematic, detailed and general constructive theory of probability theory and stochastic processes. It is the first extended account of this theory: almost all of the constructive existence and continuity theorems that permeate the book are original. It also contains results and methods hitherto unknown in the constructive and nonconstructive settings. The text features logic only in the common sense and, beyond a certain mathematical maturity, requires no prior training in either constructive mathematics or probability theory. It will thus be accessible and of interest, both to probabilists interested in the foundations of their speciality and to constructive mathematicians who wish to see Bishop's theory applied to a particular field.

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.

Advances In Proof Theory

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Author : Reinhard Kahle
language : en
Publisher: Birkhäuser
Release Date : 2016-05-04

Advances In Proof Theory written by Reinhard Kahle and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-04 with Mathematics categories.

The aim of this volume is to collect original contributions by the best specialists from the area of proof theory, constructivity, and computation and discuss recent trends and results in these areas. Some emphasis will be put on ordinal analysis, reductive proof theory, explicit mathematics and type-theoretic formalisms, and abstract computations. The volume is dedicated to the 60th birthday of Professor Gerhard Jäger, who has been instrumental in shaping and promoting logic in Switzerland for the last 25 years. It comprises contributions from the symposium “Advances in Proof Theory”, which was held in Bern in December 2013. ​Proof theory came into being in the twenties of the last century, when it was inaugurated by David Hilbert in order to secure the foundations of mathematics. It was substantially influenced by Gödel's famous incompleteness theorems of 1930 and Gentzen's new consistency proof for the axiom system of first order number theory in 1936. Today, proof theory is a well-established branch of mathematical and philosophical logic and one of the pillars of the foundations of mathematics. Proof theory explores constructive and computational aspects of mathematical reasoning; it is particularly suitable for dealing with various questions in computer science.

Ways Of Proof Theory

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Author : Ralf Schindler
language : en
Publisher: Walter de Gruyter
Release Date : 2013-05-02

Ways Of Proof Theory written by Ralf Schindler and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-02 with Philosophy categories.

On the occasion of the retirement of Wolfram Pohlers the Institut für Mathematische Logik und Grundlagenforschung of the University of Münster organized a colloquium and a workshop which took place July 17 – 19, 2008. This event brought together proof theorists from many parts of the world who have been acting as teachers, students and collaborators of Wolfram Pohlers and who have been shaping the field of proof theory over the years. The present volume collects papers by the speakers of the colloquium and workshop; and they produce a documentation of the state of the art of contemporary proof theory.

Bibliography Of Mathematical Logic

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Author : Jane E. Kister
language : en
Publisher: Springer
Release Date : 1987-06-01

Bibliography Of Mathematical Logic written by Jane E. Kister and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-06-01 with Mathematics categories.

Gert H. Müller The growth of the number of publications in almost all scientific areas, as in the area of (mathematical) logic, is taken as a sign of our scientifically minded culture, but it also has a terrifying aspect. In addition, given the rapidly growing sophistica tion, specialization and hence subdivision of logic, researchers, students and teachers may have a hard time getting an overview of the existing literature, partic ularly if they do not have an extensive library available in their neighbourhood: they simply do not even know what to ask for! More specifically, if someone vaguely knows that something vaguely connected with his interests exists some where in the literature, he may not be able to find it even by searching through the publications scattered in the review journals. Answering this challenge was and is the central motivation for compiling this Bibliography. The Bibliography comprises (presently) the following six volumes (listed with the corresponding Editors): 1. Classical Logic W. Rautenberg 11. Non-c1assical Logics W. Rautenberg III. Model Theory H. -D. Ebbinghaus IV. Recursion Theory P. G. Hinman V. Set Theory A. R. Blass VI. ProofTheory; Constructive Mathematics J. E. Kister; D. van Dalen & A. S. Troelstra.

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.

An Introduction To Proof Theory

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Author : Paolo Mancosu
language : en
Publisher: Oxford University Press
Release Date : 2021

An Introduction To Proof Theory written by Paolo Mancosu 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 2021 with Mathematics categories.

"Proof theory is a central area of mathematical logic of special interest to philosophy . It has its roots in the foundational debate of the 1920s, in particular, in Hilbert's program in the philosophy of mathematics, which called for a formalization of mathematics, as well as for a proof, using philosophically unproblematic, "finitary" means, that these systems are free from contradiction. Structural proof theory investigates the structure and properties of proofs in different formal deductive systems, including axiomatic derivations, natural deduction, and the sequent calculus. Central results in structural proof theory are the normalization theorem for natural deduction, proved here for both intuitionistic and classical logic, and the cut-elimination theorem for the sequent calculus. In formal systems of number theory formulated in the sequent calculus, the induction rule plays a central role. It can be eliminated from proofs of sequents of a certain elementary form: every proof of an atomic sequent can be transformed into a "simple" proof. This is Hilbert's central idea for giving finitary consistency proofs. The proof requires a measure of proof complexity called an ordinal notation. The branch of proof theory dealing with mathematical systems such as arithmetic thus has come to be called ordinal proof theory. The theory of ordinal notations is developed here in purely combinatorial terms, and the consistency proof for arithmetic presented in detail"--