Mathematical Logic, Ebbinghaus, Heinz-Dieter Flum, Joerg Thomas, Wolfgang
Автор: Nederpelt Название: Type Theory and Formal Proof ISBN: 110703650X ISBN-13(EAN): 9781107036505 Издательство: Cambridge Academ Рейтинг: Цена: 70740.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Type theory is a fast-evolving field at the crossroads of logic, computer science and mathematics. This book provides a gentle step-by-step introduction in the art of formalizing mathematics on the basis of type theory. It is suitable for a broad audience, ranging from undergraduate students to researchers.
Автор: Barendregt Название: Lambda Calculus with Types ISBN: 0521766141 ISBN-13(EAN): 9780521766142 Издательство: Cambridge Academ Рейтинг: Цена: 85530.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Typed lambda calculus is used in functional programming (Haskell, Clean) and proof assistants (Coq, Isabelle, HOL), which are used to design and verify IT products and mathematical proofs. This book reveals unexpected mathematical beauty in three classes of typing: simple types, recursive types and intersection types. Numerous exercises are provided.
Автор: Hayashi Masahito Название: Quantum Information Theory: Mathematical Foundation ISBN: 3662570327 ISBN-13(EAN): 9783662570326 Издательство: Springer Рейтинг: Цена: 79190.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Invitation to Quantum Information Theory.- History of Quantum Information Theory.- The Structure of this Text.- Mathematical Formulation of Quantum Systems.- Information Quantities and Parameter Estimation in Classical Systems.- Quantum Hypothesis Testing and Discrimination of Quantum States.- Classical-Quantum Channel Coding (Message Transmission).- State Evolution and Trace-Preserving Completely Positive Maps.- Quantum Information Geometry and Quantum Estimation.- Quantum Measurements and State Reduction.- Entanglement and Locality Restrictions.- Analysis of Quantum Communication Protocols.
Автор: Herbert Enderton Название: A Mathematical Introduction to Logic, ISBN: 0122384520 ISBN-13(EAN): 9780122384523 Издательство: Elsevier Science Рейтинг: Цена: 93290.00 T Наличие на складе: Поставка под заказ. Описание: Presents material on computer science issues such as computational complexity and database queries, with coverage of introductory material such as sets. This book helps instructors with choices in how they use the textbook in courses, and reduced mathematical rigour to fit the needs of undergraduate students.
Автор: Mendelson Elliott Название: Introduction to Mathematical Logic ISBN: 1482237725 ISBN-13(EAN): 9781482237726 Издательство: Taylor&Francis Рейтинг: Цена: 54560.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
The new edition of this classic textbook, Introduction to Mathematical Logic, Sixth Edition explores the principal topics of mathematical logic. It covers propositional logic, first-order logic, first-order number theory, axiomatic set theory, and the theory of computability. The text also discusses the major results of G del, Church, Kleene, Rosser, and Turing.
The sixth edition incorporates recent work on G del's second incompleteness theorem as well as restoring an appendix on consistency proofs for first-order arithmetic. This appendix last appeared in the first edition. It is offered in the new edition for historical considerations. The text also offers historical perspectives and many new exercises of varying difficulty, which motivate and lead students to an in-depth, practical understanding of the material.
Автор: Lakatos Название: Proofs and Refutations ISBN: 1107534054 ISBN-13(EAN): 9781107534056 Издательство: Cambridge Academ Рейтинг: Цена: 22170.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Imre Lakatos`s influential and enduring work on the nature of mathematic discovery and development continues to be relevant to philosophers of mathematics. Including a specially commissioned preface written by Paolo Mancosu, and presented in a fresh twenty-first-century series livery, it is now available for a new generation of readers.
Автор: Brendan Fong, David I. Spivak Название: An Invitation to Applied Category Theory: Seven Sketches in Compositionality ISBN: 1108711820 ISBN-13(EAN): 9781108711821 Издательство: Cambridge Academ Рейтинг: Цена: 48570.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Category theory reveals commonalities between structures of all sorts. This self-contained tour of applied category theory shows its potential in science, engineering, and beyond. Each chapter discusses a real-world application using category-theoretic tools, all of which are introduced in an accessible way with many examples and exercises.
This book is a brief and focused introduction to the reverse mathematics and computability theory of combinatorial principles, an area of research which has seen a particular surge of activity in the last few years. It provides an overview of some fundamental ideas and techniques, and enough context to make it possible for students with at least a basic knowledge of computability theory and proof theory to appreciate the exciting advances currently happening in the area, and perhaps make contributions of their own. It adopts a case-study approach, using the study of versions of Ramsey's Theorem (for colorings of tuples of natural numbers) and related principles as illustrations of various aspects of computability theoretic and reverse mathematical analysis. This book contains many exercises and open questions.
Автор: Diller, Justus (univ Of Munster, Germany) Название: Functional interpretations: from the dialectica interpretation to interpretations of classical and constructive set theory ISBN: 9814551392 ISBN-13(EAN): 9789814551397 Издательство: World Scientific Publishing Рейтинг: Цена: 95040.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book gives a detailed treatment of functional interpretations of arithmetic, analysis, and set theory. The subject goes back to G del's Dialectica interpretation of Heyting arithmetic which replaces nested quantification by higher type operations and thus reduces the consistency problem for arithmetic to the problem of computability of primitive recursive functionals of finite types. Regular functional interpretations, in particular the Dialectica interpretation and its generalization to finite types, the Diller-Nahm interpretation, are studied on Heyting as well as Peano arithmetic in finite types and extended to functional interpretations of constructive as well as classical systems of analysis and set theory. Kreisel's modified realization and Troelstra's hybrids of it are presented as interpretations of Heyting arithmetic and extended to constructive set theory, both in finite types. They serve as background for the construction of hybrids of the Diller-Nahm interpretation of Heyting arithmetic and constructive set theory, again in finite types. All these functional interpretations yield relative consistency results and closure under relevant rules of the theories in question as well as axiomatic characterizations of the functional translations.
Автор: Toth, Herbert, Название: Relations : concrete, abstract, and applied : ISBN: 9811220344 ISBN-13(EAN): 9789811220340 Издательство: World Scientific Publishing Рейтинг: Цена: 163680.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
The book is intended as an invitation to the topic of relations on a rather general basis. It fills the gap between the basic knowledge offered in countless introductory papers and books (usually comprising orders and equivalences) and the highly specialized monographs on mainly relation algebras, many-valued (fuzzy) relations, or graphs. This is done not only by presenting theoretical results but also by giving hints to some of the many interesting application areas (also including their respective theoretical basics).
This book is a new -- and the first of its kind -- compilation of known results on binary relations. It offers relational concepts in both reasonable depth and broadness, and also provides insight into the vast diversity of theoretical results as well as application possibilities beyond the commonly known examples.
This book is unique by the spectrum of the topics it handles. As indicated in its title these are:
Concrete aspects are covered in detail in Part 2 for two-valued, and in Part 3 for many-valued relations. Various kinds of relations and their properties are presented in the familiar form of first order formulas, but mainly algebraically in the point-free version as used in the so-called calculus of relations.
Abstract points of view are the content of Part 4: The connections of relations to semigroups, as well as the concept of relation algebras, and how relations are handled within category theory are presented in some detail.
Applied relations in Part 5 give a broad spectrum of classical and newer topics where relations of various kinds play a dominant role. This way, readers should get an idea how diverse the possibililties are where relations can be used, and how mighty their modeling abilities turn out to be.
Автор: Church, Alonzo Название: Introduction to mathematical logic ISBN: 0691029067 ISBN-13(EAN): 9780691029061 Издательство: Wiley Рейтинг: Цена: 86590.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Logic is sometimes called the foundation of mathematics: the logician studies the kinds of reasoning used in the individual steps of a proof. Alonzo Church`s contributions to number theory and theories of algorithms and computability laid the theoretical foundations of computer science. This book is a basic source for understanding formal logic.
Название: Forcing for Mathematicians ISBN: 9814566004 ISBN-13(EAN): 9789814566001 Издательство: World Scientific Publishing Рейтинг: Цена: 57030.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Ever since Paul Cohen's spectacular use of the forcing concept to prove the independence of the continuum hypothesis from the standard axioms of set theory, forcing has been seen by the general mathematical community as a subject of great intrinsic interest but one that is technically so forbidding that it is only accessible to specialists. In the past decade, a series of remarkable solutions to long-standing problems in C*-algebra using set-theoretic methods, many achieved by the author and his collaborators, have generated new interest in this subject. This is the first book aimed at explaining forcing to general mathematicians. It simultaneously makes the subject broadly accessible by explaining it in a clear, simple manner, and surveys advanced applications of set theory to mainstream topics.
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