Author : J. Barwise
Publisher : Cambridge University Press
Page : 912 pages
File Size : 38,9 MB
Release : 2017-03-02
Category : Mathematics
ISBN : 1107168252
This book brings together several directions of work in model theory between the late 1950s and early 1980s.
Author : Thomas Drucker
Publisher : Springer Science & Business Media
Page : 218 pages
File Size : 15,94 MB
Release : 2008-01-04
Category : Mathematics
ISBN : 0817647686
This 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
Page : 480 pages
File Size : 45,49 MB
Release : 2011-12-15
Category : Mathematics
ISBN : 1139504169
Driven 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 : Stephen George Simpson
Publisher : Cambridge University Press
Page : 461 pages
File Size : 42,68 MB
Release : 2009-05-29
Category : Mathematics
ISBN : 052188439X
This volume examines appropriate axioms for mathematics to prove particular theorems in core areas.
Author :
Publisher :
Page : pages
File Size : 37,57 MB
Release : 1969
Category :
ISBN :
"The Perspectives in Logic series publishes substantial, high-quality books whose central theme lies in any area or aspect of logic. Books that present new material not now available in book form are particularly welcome. The series ranges from introductory texts suitable for beginning graduate courses to specialized monographs at the frontiers of research. Each book offers an illuminating perspective for its intended audience. The ASL is committed to making books in the Perspectives in Logic series available at a reasonable cost, and intends to keep them available in print or electronic form indefinitely. This series is the successor to the series Perspectives in Mathematical Logic, which was founded in 1969 by the Omega Group, consisting of R. O. Gandy, H. Hermes, A. Levy, G. H. Müller, G. E. Sacks and D. S. Scott. This group was initially sponsored by a grant from the Stiftung Volkswagenwerk and the series appeared under the auspices of the Heidelberger Akademie der Wissenschaften. From 1986 to 2001, Perspectives in Mathematical Logic was published by Springer-Verlag under editorial direction of the Association for Symbolic Logic. In 2001 the ASL assumed full responsibility for the series and broadened its scope to include all of logic. It is now published jointly with Cambridge University Press as Perspectives in Logic." -- Project Euclid.
Author : Robert F. Lusch
Publisher : Cambridge University Press
Page : 253 pages
File Size : 46,52 MB
Release : 2014-01-30
Category : Business & Economics
ISBN : 1139952021
In 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 : Henk Barendregt
Publisher : Cambridge University Press
Page : 969 pages
File Size : 15,11 MB
Release : 2013-06-20
Category : Mathematics
ISBN : 1107276349
This 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 : Antonio Montalbán
Publisher : Cambridge University Press
Page : 214 pages
File Size : 23,99 MB
Release : 2021-06-24
Category : Mathematics
ISBN : 1108534422
In 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 : Joseph Mileti
Publisher : Cambridge University Press
Page : 517 pages
File Size : 28,35 MB
Release : 2022-09-22
Category : Mathematics
ISBN : 1108833144
This textbook gives a comprehensive and modern introduction to mathematical logic at the upper-undergraduate and beginning graduate level.
Author : Gil Sagi
Publisher : Cambridge University Press
Page : 316 pages
File Size : 37,31 MB
Release : 2021-09-09
Category : Mathematics
ISBN : 1108529828
This 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.
