A Model–Theoretic Approach to Proof Theory, Henryk Kotlarski; Zofia Adamowicz; Teresa Bigorajs
Автор: Henryk Kotlarski; Zofia Adamowicz; Teresa Bigorajs Название: A Model–Theoretic Approach to Proof Theory ISBN: 3030289206 ISBN-13(EAN): 9783030289201 Издательство: Springer Рейтинг: Цена: 46570.00 T Наличие на складе: Нет в наличии. Описание: This book presents a detailed treatment of ordinal combinatorics of large sets tailored for independence results. It uses model theoretic and combinatorial methods to obtain results in proof theory, such as incompleteness theorems or a description of the provably total functions of a theory.In the first chapter, the authors first discusses ordinal combinatorics of finite sets in the style of Ketonen and Solovay. This provides a background for an analysis of subsystems of Peano Arithmetic as well as for combinatorial independence results. Next, the volume examines a variety of proofs of G?del's incompleteness theorems. The presented proofs differ strongly in nature. They show various aspects of incompleteness phenomena. In additon, coverage introduces some classical methods like the arithmetized completeness theorem, satisfaction predicates or partial satisfaction classes. It also applies them in many contexts. The fourth chapter defines the method of indicators for obtaining independence results. It shows what amount of transfinite induction we have in fragments of Peano arithmetic. Then, it uses combinatorics of large sets of the first chapter to show independence results. The last chapter considers nonstandard satisfaction classes. It presents some of the classical theorems related to them. In particular, it covers the results by S. Smith on definability in the language with a satisfaction class and on models without a satisfaction class. Overall, the book's content lies on the border between combinatorics, proof theory, and model theory of arithmetic. It offers readers a distinctive approach towards independence results by model-theoretic methods.
Автор: Saccoman John T., Suffel Charles L., Gross Daniel Название: Spanning Tree Results for Graphs and Multigraphs: A Matrix-Theoretic Approach ISBN: 9814566039 ISBN-13(EAN): 9789814566032 Издательство: World Scientific Publishing Рейтинг: Цена: 74970.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
This book is concerned with the optimization problem of maximizing the number of spanning trees of a multigraph. Since a spanning tree is a minimally connected subgraph, graphs and multigraphs having more of these are, in some sense, immune to disconnection by edge failure. We employ a matrix-theoretic approach to the calculation of the number of spanning trees.
The authors envision this as a research aid that is of particular interest to graduate students or advanced undergraduate students and researchers in the area of network reliability theory. This would encompass graph theorists of all stripes, including mathematicians, computer scientists, electrical and computer engineers, and operations researchers.
Errata(s)
Автор: Barwise Название: Model-Theoretic Logics ISBN: 1107168252 ISBN-13(EAN): 9781107168251 Издательство: Cambridge Academ Рейтинг: Цена: 200640.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: In this volume the authors bring together several directions of work in model theory between the late 1950s and early 1980s. It contains expository papers by pre-eminent researchers on advanced topics in model theory. Many chapters can be read independently.
Автор: E.B. Ruttkamp Название: A Model-Theoretic Realist Interpretation of Science ISBN: 9048160669 ISBN-13(EAN): 9789048160662 Издательство: Springer Рейтинг: Цена: 130430.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This text can be read by specialists working in philosophy of science or formal semantics, by logicians working on the structure of theories, and by students in philosophy of science - this text offers a thorough introduction to non-statement accounts of sciences as well as a discussion of the traditional statement account of science.
Автор: Thomas Piecha; Peter Schroeder-Heister Название: Advances in Proof-Theoretic Semantics ISBN: 3319226851 ISBN-13(EAN): 9783319226859 Издательство: Springer Рейтинг: Цена: 46570.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
This volume is the first ever collection devoted to the field of proof-theoretic semantics. Contributions address topics including the systematics of introduction and elimination rules and proofs of normalization, the categorial characterization of deductions, the relation between Heyting's and Gentzen's approaches to meaning, knowability paradoxes, proof-theoretic foundations of set theory, Dummett's justification of logical laws, Kreisel's theory of constructions, paradoxical reasoning, and the defence of model theory.
The field of proof-theoretic semantics has existed for almost 50 years, but the term itself was proposed by Schroeder-Heister in the 1980s. Proof-theoretic semantics explains the meaning of linguistic expressions in general and of logical constants in particular in terms of the notion of proof. This volume emerges from presentations at the Second International Conference on Proof-Theoretic Semantics in T bingen in 2013, where contributing authors were asked to provide a self-contained description and analysis of a significant research question in this area. The contributions are representative of the field and should be of interest to logicians, philosophers, and mathematicians alike.
Автор: Thomas Piecha; Peter Schroeder-Heister Название: Advances in Proof-Theoretic Semantics ISBN: 3319367811 ISBN-13(EAN): 9783319367811 Издательство: Springer Рейтинг: Цена: 46570.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Chapter 1. Introduction; Thomas Piecha & Peter-Schroeder-Heister.- Chapter 2. On Brouwer-Heyting-Kolmogorov provability semantics; Sergei N. Artлmov.- Chapter 3. Two Ways of General Proof Theory; Kosta Dosen.- Chapter 4. Generalised elimination rules; Roy Dyckhoff.- Chapter 5. On the proof theoretic foundations of set theory; Lars Hallnдs.- Chapter 6. The choice of semantics as a methodological question; Wilfrid Hodges.- Chapter 7. The mode of presentation; Reinhard Kahle.- Chapter 8. Remarks on relations between Gentzen and Heyting inspired PTS; Dag Prawitz.- Chapter 9. Unification of logics by reflection; Giovanni Sambin.- Chapter 10. BHK and Brouwer's Theory of the Creative Subject; Gцran Sundholm.- Chapter 11. Compositional semantics for predicate logic: Eliminating bound variables from formulas and deductions; William W. Tait.- Chapter 12. Intuitionism, the Paradox of Knowability and Empirical Negation; Gabriele Usberti.- Chapter 13. Explicit composition and its application in normalization proofs; Jan von Plato.- Chapter 14. A two-sorted typed lambda-calculus; Heinrich Wansing.- Chapter 15. Kreisel's second clause and the Theory of Constructions; Walter Dean & Hidenori Kurokawa.- Chapter 16. On Paradoxes in Proof-Theoretic Semantics; Yoshihiro Maruyama.
Автор: Hinman Название: Recursion-Theoretic Hierarchies ISBN: 1107168244 ISBN-13(EAN): 9781107168244 Издательство: Cambridge Academ Рейтинг: Цена: 159450.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The theory set out in this volume is the result of the meeting and common development of two currents of mathematical research: descriptive set theory and recursion theory. The author develops a general theory from which the results of both areas can be derived, making the common themes clear.
Автор: Fajardo William, Gallego Claudia, Lezama Oswaldo Название: Skew Pbw Extensions: Ring and Module-Theoretic Properties, Matrix and Grцbner Methods, and Applications ISBN: 3030533778 ISBN-13(EAN): 9783030533779 Издательство: Springer Цена: 121110.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Preface.- I Ring and Module-Theoretic Properties of Skew PBW Extensions.- II Projective Modules Over Skew PBW Extensions.- III Matrix and Grцbner Methods for Skew PBW Extensions.- IV Applications: The Noncommutative AlgebraicGeometry of Skew PBW Extensions.- References.
Автор: Kueker Название: Mathematical Logic and Theoretical Computer Science ISBN: 0824777468 ISBN-13(EAN): 9780824777463 Издательство: Taylor&Francis Рейтинг: Цена: 265410.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book includes articles on denotational semanitcs, recursion theoretic aspects of computer science, model theory and algebra, automath and automated reasoning, stability theory, topoi and mathematics, and topoi and logic. It is intended for mathematical logicians and computer scientists.
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