Ordinal Computability: An Introduction to Infinitary Machines, Merlin Carl
Автор: Barry S. Cooper; Sergei S. Goncharov Название: Computability and Models ISBN: 1461352258 ISBN-13(EAN): 9781461352259 Издательство: Springer Рейтинг: Цена: 13974.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: There are also articles concerned with the computability of aspects of familiar mathematical structures, and - a return to the sort of basic underlying questions considered by Alan Turing in the early days of the subject - an article giving a new perspective on computability in the real world.
Автор: Nourani Название: Algebraic Computability and Enumeration Models ISBN: 1771882476 ISBN-13(EAN): 9781771882477 Издательство: Taylor&Francis Рейтинг: Цена: 21437.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This book, Algebraic Computability and Enumeration Models: Recursion Theory and Descriptive Complexity, presents new techniques with functorial models to address important areas on pure mathematics and computability theory from the algebraic viewpoint. The reader is first introduced to categories and functorial models, with Kleene algebra examples for languages. Functorial models for Peano arithmetic are described toward important computational complexity areas on a Hilbert program, leading to computability with initial models. Infinite language categories are also introduced to explain descriptive complexity with recursive computability with admissible sets and urelements.
Algebraic and categorical realizability is staged on several levels, addressing new computability questions with omitting types realizably. Further applications to computing with ultrafilters on sets and Turing degree computability are examined. Functorial models computability is presented with algebraic trees realizing intuitionistic types of models. New homotopy techniques are applied to Marin Lof types of computations with model categories. Functorial computability, induction, and recursion are examined in view of the above, presenting new computability techniques with monad transformations and projective sets.
This informative volume will give readers a complete new feel for models, computability, recursion sets, complexity, and realizability. This book pulls together functorial thoughts, models, computability, sets, recursion, arithmetic hierarchy, filters, with real tree computing areas, presented in a very intuitive manner for university teaching, with exercises for every chapter. The book will also prove valuable for faculty in computer science and mathematics.
Автор: Jon Barwise Название: The Syntax and Semantics of Infinitary Languages ISBN: 3540042423 ISBN-13(EAN): 9783540042426 Издательство: Springer Рейтинг: Цена: 6288.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: Marker Название: Lectures on Infinitary Model Theory ISBN: 1107181933 ISBN-13(EAN): 9781107181939 Издательство: Cambridge Academ Рейтинг: Цена: 18216.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book is the first modern introduction to the logic of infinitary languages in forty years, and is aimed at graduate students and researchers in all areas of mathematical logic. Connections between infinitary model theory and other branches of mathematical logic, and applications to algebra and algebraic geometry are both comprehensively explored.
Автор: Adam Day; Michael Fellows; Noam Greenberg; Bakhady Название: Computability and Complexity ISBN: 3319500619 ISBN-13(EAN): 9783319500614 Издательство: Springer Рейтинг: Цена: 13974.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The volume contains 42 papers presenting original unpublished research, or expository and survey results in Turing degrees, computably enumerable sets, computable algebra, computable model theory, algorithmic randomness, reverse mathematics, and parameterized complexity, all areas in which Rod Downey has had significant interests and influence.
Автор: Pippenger Название: Theories of Computability ISBN: 0521553806 ISBN-13(EAN): 9780521553803 Издательство: Cambridge Academ Рейтинг: Цена: 14731.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book gives an introduction to theories of computability from a mathematically sophisticated point of view. It treats not only `the` theory of computability, but also a variety of other theories. Each topic is taken from the beginning and developed to a point at which the results can be appreciated.
Автор: C.S. Calude; M.J. Dinneen; S. Sburlan Название: Combinatorics, Computability and Logic ISBN: 1852335262 ISBN-13(EAN): 9781852335267 Издательство: Springer Рейтинг: Цена: 18167.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This volume contains the papers presented at the Third Combinatorics, Computability and Logic (DMTCS`01) conference, These papers cover topics such as abstract data types and specifications algorithms and data structures automata and formal languages computability among others.
Автор: Pour-El Название: Computability in Analysis and Physics ISBN: 1107168449 ISBN-13(EAN): 9781107168442 Издательство: Cambridge Academ Рейтинг: Цена: 18216.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This is the first graduate-level treatment of computable analysis within the tradition of classical mathematical reasoning. The authors are concerned with the computability or noncomputability of standard processes in analysis and physics. The book is self-contained and serves well as an introduction to research in this area.
Автор: Sernadas Amilcar, Sernadas Cristina, Rasga Joao Название: A Mathematical Primer on Computability ISBN: 1848902964 ISBN-13(EAN): 9781848902961 Издательство: Неизвестно Цена: 3954.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
The book provides a self-contained introduction to computability theory for advanced undergraduate or early graduate students of mathematics and computer science. The technical material is illustrated with plenty of examples, problems with fully worked solutions as well as a range of proposed exercises.
Part I is centered around fundamental computability notions and results, starting with the pillar concepts of computational model (an abstract high-level programming language), computable function, decidable and listable set, proper universal function, decision problem and the reduction technique for transferring decidability and listability properties. The essential results namely Rice's Theorem, Rice-Shapiro's Theorem, Rice-Shapiro-McNaughton-Myhill's Theorem as well as Rogers' Theorem and the Recursion Theorem are presented and illustrated. Many-to-one reducibility and many-to-one degrees are investigated. A short introduction to computation with oracles is also included. Computable as well as non-computable operators are introduced as well as monotonic and finitary operators. The relationship between them is discussed, in particular via Myhill-Shepherdson's Theorem. Kleene's Least Fixed Point Theorem is also presented. Finally, Part I terminates with a briefi ng on the Turing computational model, Turing reducibility and Turing degrees.
Part II of the book concentrates on applications of computability in several areas namely in logic (undecidability of arithmetic, satisfiability in propositional logic, decidability in modal logic), Euclidean geometry, graphs and Kolmogorov complexity. Nevertheless no previous knowledge of these subjects is required. The essential details for understanding the applications are provided.
Автор: Ershov, I?U?rii? Leonidovich. Название: Definability and computability / ISBN: 0306110393 ISBN-13(EAN): 9780306110399 Издательство: Springer Рейтинг: Цена: 32004.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: In this book, Yurii L. Ershov posits the view that computability-in the broadest sense-can be regarded as the Sigma-definability in the suitable sets. He presents a new approach to providing the G del incompleteness theorem based on systematic use of the formulas with the restricted quantifiers. The volume also includes a novel exposition on the foundations of the theory of admissible sets with urelements, using the Gandy theorem throughout the theory's development. Other topics discussed are forcing, Sigma-definability, dynamic logic, and Sigma-predicates of finite types.
Автор: Stefania Centrone; Sara Negri; Deniz Sarikaya; Pet Название: Mathesis Universalis, Computability and Proof ISBN: 3030204464 ISBN-13(EAN): 9783030204464 Издательство: Springer Рейтинг: Цена: 13974.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 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” (“Gr?nde”) 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.
Автор: Rogers, H. Название: Theory of recursive functions and effective computability / ISBN: 0262680521 ISBN-13(EAN): 9780262680523 Издательство: MIT Press Рейтинг: Цена: 8465.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: (Reprint of the 1967 edition)
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