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Author: J. Barwise
Publisher: Cambridge University Press
Published: 2017-03-02
Total Pages: 912
ISBN-13: 1107168252
DOWNLOAD EBOOKThis book brings together several directions of work in model theory between the late 1950s and early 1980s.
Author: Stephen George Simpson
Publisher: Cambridge University Press
Published: 2009-05-29
Total Pages: 461
ISBN-13: 052188439X
DOWNLOAD EBOOKThis volume examines appropriate axioms for mathematics to prove particular theorems in core areas.
Author: Thomas Drucker
Publisher: Springer Science & Business Media
Published: 2009-05-21
Total Pages: 218
ISBN-13: 0817647694
DOWNLOAD EBOOKThis volume offers insights into the development of mathematical logic over the last century. Arising from a special session of the history of logic at an American Mathematical Society meeting, the chapters explore technical innovations, the philosophical consequences of work during the period, and the historical and social context in which the logicians worked. The discussions herein will appeal to mathematical logicians and historians of mathematics, as well as philosophers and historians of science.
Author: Helmut Schwichtenberg
Publisher: Cambridge University Press
Published: 2011-12-15
Total Pages: 480
ISBN-13: 1139504169
DOWNLOAD EBOOKDriven by the question, 'What is the computational content of a (formal) proof?', this book studies fundamental interactions between proof theory and computability. It provides a unique self-contained text for advanced students and researchers in mathematical logic and computer science. Part I covers basic proof theory, computability and Gödel's theorems. Part II studies and classifies provable recursion in classical systems, from fragments of Peano arithmetic up to Π11–CA0. Ordinal analysis and the (Schwichtenberg–Wainer) subrecursive hierarchies play a central role and are used in proving the 'modified finite Ramsey' and 'extended Kruskal' independence results for PA and Π11–CA0. Part III develops the theoretical underpinnings of the first author's proof assistant MINLOG. Three chapters cover higher-type computability via information systems, a constructive theory TCF of computable functionals, realizability, Dialectica interpretation, computationally significant quantifiers and connectives and polytime complexity in a two-sorted, higher-type arithmetic with linear logic.
Author: Henk Barendregt
Publisher: Cambridge University Press
Published: 2013-06-20
Total Pages: 969
ISBN-13: 1107276349
DOWNLOAD EBOOKThis handbook with exercises reveals in formalisms, hitherto mainly used for hardware and software design and verification, unexpected mathematical beauty. The lambda calculus forms a prototype universal programming language, which in its untyped version is related to Lisp, and was treated in the first author's classic The Lambda Calculus (1984). The formalism has since been extended with types and used in functional programming (Haskell, Clean) and proof assistants (Coq, Isabelle, HOL), used in designing and verifying IT products and mathematical proofs. In this book, the authors focus on three classes of typing for lambda terms: simple types, recursive types and intersection types. It is in these three formalisms of terms and types that the unexpected mathematical beauty is revealed. The treatment is authoritative and comprehensive, complemented by an exhaustive bibliography, and numerous exercises are provided to deepen the readers' understanding and increase their confidence using types.
Author: Robert F. Lusch
Publisher: Cambridge University Press
Published: 2014-01-30
Total Pages: 253
ISBN-13: 1139952021
DOWNLOAD EBOOKIn 2004, Robert F. Lusch and Stephen L. Vargo published their groundbreaking article on the evolution of marketing theory and practice toward 'service-dominant (S-D) logic', describing the shift from a product-centred view of markets to a service-led model. Now, in this keenly anticipated book, the authors present a thorough primer on the principles and applications of S-D logic. They describe a clear alternative to the dominant worldview of the heavily planned, production-oriented, profit-maximizing firm, presenting a coherent, organizing framework based on ten foundational premises. The foundational premises of S-D logic have much wider implications beyond marketing for the future of the firm, transcending different industries and contexts, and will provide readers with a deeper sense of why the exchange of service is the fundamental basis of all social and economic exchange. This accessible book will appeal to students, as well as to researchers and practitioners.
Author: Gil Sagi
Publisher: Cambridge University Press
Published: 2021-09-09
Total Pages: 316
ISBN-13: 1108529828
DOWNLOAD EBOOKThis collection of new essays presents cutting-edge research on the semantic conception of logic, the invariance criteria of logicality, grammaticality, and logical truth. Contributors explore the history of the semantic tradition, starting with Tarski, and its historical applications, while central criticisms of the tradition, and especially the use of invariance criteria to explain logicality, are revisited by the original participants in that debate. Other essays discuss more recent criticism of the approach, and researchers from mathematics and linguistics weigh in on the role of the semantic tradition in their disciplines. This book will be invaluable to philosophers and logicians alike.
Author: Gerald E. Sacks
Publisher: Cambridge University Press
Published: 2017-03-02
Total Pages: 361
ISBN-13: 1107168430
DOWNLOAD EBOOKThis almost self-contained introduction to higher recursion theory is essential reading for all researchers in the field.
Author: Antonio Montalbán
Publisher: Cambridge University Press
Published: 2021-06-24
Total Pages: 214
ISBN-13: 1108534422
DOWNLOAD EBOOKIn mathematics, we know there are some concepts - objects, constructions, structures, proofs - that are more complex and difficult to describe than others. Computable structure theory quantifies and studies the complexity of mathematical structures, structures such as graphs, groups, and orderings. Written by a contemporary expert in the subject, this is the first full monograph on computable structure theory in 20 years. Aimed at graduate students and researchers in mathematical logic, it brings new results of the author together with many older results that were previously scattered across the literature and presents them all in a coherent framework, making it easier for the reader to learn the main results and techniques in the area for application in their own research. This volume focuses on countable structures whose complexity can be measured within arithmetic; a forthcoming second volume will study structures beyond arithmetic.
Author: Eugenio G. Omodeo
Publisher: Springer
Published: 2017-05-11
Total Pages: 283
ISBN-13: 3319549812
DOWNLOAD EBOOKThis treatise presents an integrated perspective on the interplay of set theory and graph theory, providing an extensive selection of examples that highlight how methods from one theory can be used to better solve problems originated in the other. Features: explores the interrelationships between sets and graphs and their applications to finite combinatorics; introduces the fundamental graph-theoretical notions from the standpoint of both set theory and dyadic logic, and presents a discussion on set universes; explains how sets can conveniently model graphs, discussing set graphs and set-theoretic representations of claw-free graphs; investigates when it is convenient to represent sets by graphs, covering counting and encoding problems, the random generation of sets, and the analysis of infinite sets; presents excerpts of formal proofs concerning graphs, whose correctness was verified by means of an automated proof-assistant; contains numerous exercises, examples, definitions, problems and insight panels.
