Essays in Constructive Mathematics, Harold M. Edwards

Автор: F. Richman
Название: Constructive Mathematics
ISBN: 3540108505 ISBN-13(EAN): 9783540108504
Издательство: Springer
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Автор: Anna Horsk?
Название: Where is the G?del-point hiding: Gentzen`s Consistency Proof of 1936 and His Representation of Constructive Ordinals
ISBN: 3319021702 ISBN-13(EAN): 9783319021706
Издательство: Springer
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Описание: This book explains the first published consistency proof of PA. A notable aspect of the proof is the representation of ordinal numbers that was developed by Gentzen. The topic should interest researchers and students who work on proof theory, history of proof theory or Hilbert`s program and who do not mind reading mathematical texts.ГЇВїВЅ

Автор: Mines
Название: A Course in Constructive Algebra
ISBN: 0387966404 ISBN-13(EAN): 9780387966403
Издательство: Springer
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Описание: Presents the fundamental structures of modern algebra from a constructive point of view. This book contains basic notions, and also covers PID`s, field theory (including Galois theory), factorisation of polynomials, noetherian rings, valuation theory, and Dedekind domains.

Автор: Ershov, I?U?rii? Leonidovich.
Название: Constructive models /
ISBN: 0306110660 ISBN-13(EAN): 9780306110665
Издательство: Springer
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Описание: This work gives an exposition of the modern theory of constructive models and describes methods and approaches developed by representatives of the Siberian school of algebra and logic and some other researchers (in particular, Nerode and his colleagues).

Автор: Vladimir F. Demyanov; Panos M. Pardalos; Mikhail B
Название: Constructive Nonsmooth Analysis and Related Topics
ISBN: 1493946315 ISBN-13(EAN): 9781493946310
Издательство: Springer
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Описание: This volume contains papers from the International Conference on Constructive Nonsmooth Analysis (CNSA) held in St. Petersburg, Russia, June 2012. It explores this powerful instrument in applied mathematics.

Автор: Yengui, Ihsen
Название: Constructive commutative algebra
ISBN: 3319194933 ISBN-13(EAN): 9783319194936
Издательство: Springer
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Описание:

The main goal of this book is to find the constructive content hidden in abstract proofs of concrete theorems in Commutative Algebra, especially in well-known theorems concerning projective modules over polynomial rings (mainly the Quillen-Suslin theorem) and syzygies of multivariate polynomials with coefficients in a valuation ring.

Simple and constructive proofs of some results in the theory of projective modules over polynomial rings are also given, and light is cast upon recent progress on the Hermite ring and Gr bner ring conjectures. New conjectures on unimodular completion arising from our constructive approach to the unimodular completion problem are presented.

Constructive algebra can be understood as a first preprocessing step for computer algebra that leads to the discovery of general algorithms, even if they are sometimes not efficient. From a logical point of view, the dynamical evaluation gives a constructive substitute for two highly nonconstructive tools of abstract algebra: the Law of Excluded Middle and Zorn's Lemma. For instance, these tools are required in order to construct the complete prime factorization of an ideal in a Dedekind ring, whereas the dynamical method reveals the computational content of this construction. These lecture notes follow this dynamical philosophy.

Автор: Giovanni Sommaruga
Название: Foundational Theories of Classical and Constructive Mathematics
ISBN: 9400735618 ISBN-13(EAN): 9789400735613
Издательство: Springer
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Описание: Focusing on the foundations, this volume explores both classical and constructive mathematics. Its great advantage is to extend the traditional discussion of the foundations of mathematics and to render it at the same time both subtle and more differentiated.

Автор: Nicolas Clerbout; Shahid Rahman
Название: Linking Game-Theoretical Approaches with Constructive Type Theory
ISBN: 3319190628 ISBN-13(EAN): 9783319190624
Издательство: Springer
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Описание: This title links two of the most dominant research streams in philosophy of logic, namely game theory and proof theory. The fifth chapter develops the algorithm from CTT-demonstrations to dialogical strategies.