Author : J. Barwise
Publisher : Cambridge University Press
Page : 912 pages
File Size : 37,66 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 : 12,35 MB
Release : 2009-05-21
Category : Mathematics
ISBN : 0817647694
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 : Alexander Prestel
Publisher : Springer Science & Business Media
Page : 198 pages
File Size : 15,83 MB
Release : 2011-08-21
Category : Mathematics
ISBN : 1447121767
Mathematical Logic and Model Theory: A Brief Introduction offers a streamlined yet easy-to-read introduction to mathematical logic and basic model theory. It presents, in a self-contained manner, the essential aspects of model theory needed to understand model theoretic algebra. As a profound application of model theory in algebra, the last part of this book develops a complete proof of Ax and Kochen's work on Artin's conjecture about Diophantine properties of p-adic number fields. The character of model theoretic constructions and results differ quite significantly from that commonly found in algebra, by the treatment of formulae as mathematical objects. It is therefore indispensable to first become familiar with the problems and methods of mathematical logic. Therefore, the text is divided into three parts: an introduction into mathematical logic (Chapter 1), model theory (Chapters 2 and 3), and the model theoretic treatment of several algebraic theories (Chapter 4). This book will be of interest to both advanced undergraduate and graduate students studying model theory and its applications to algebra. It may also be used for self-study.
Author : Joseph Mileti
Publisher : Cambridge University Press
Page : 517 pages
File Size : 14,55 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 : Robert I. Soare
Publisher : Springer Science & Business Media
Page : 460 pages
File Size : 30,90 MB
Release : 1999-11-01
Category : Mathematics
ISBN : 9783540152996
..."The book, written by one of the main researchers on the field, gives a complete account of the theory of r.e. degrees. .... The definitions, results and proofs are always clearly motivated and explained before the formal presentation; the proofs are described with remarkable clarity and conciseness. The book is highly recommended to everyone interested in logic. It also provides a useful background to computer scientists, in particular to theoretical computer scientists." Acta Scientiarum Mathematicarum, Ungarn 1988 ..."The main purpose of this book is to introduce the reader to the main results and to the intricacies of the current theory for the recurseively enumerable sets and degrees. The author has managed to give a coherent exposition of a rather complex and messy area of logic, and with this book degree-theory is far more accessible to students and logicians in other fields than it used to be." Zentralblatt für Mathematik, 623.1988
Author : Helmut Schwichtenberg
Publisher : Cambridge University Press
Page : 480 pages
File Size : 30,92 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 : Jon Barwise
Publisher : Cambridge University Press
Page : 409 pages
File Size : 26,39 MB
Release : 2017-03-02
Category : Mathematics
ISBN : 1107168333
This volume makes the basic facts about admissible sets accessible to logic students and specialists alike.
Author : Stephen George Simpson
Publisher : Cambridge University Press
Page : 461 pages
File Size : 33,66 MB
Release : 2009-05-29
Category : Mathematics
ISBN : 052188439X
This volume examines appropriate axioms for mathematics to prove particular theorems in core areas.
Author : Mojtaba Mojtahedi
Publisher : Springer Nature
Page : 493 pages
File Size : 46,21 MB
Release : 2021-02-09
Category : Philosophy
ISBN : 3030536548
This volume is a collection of essays in honour of Professor Mohammad Ardeshir. It examines topics which, in one way or another, are connected to the various aspects of his multidisciplinary research interests. Based on this criterion, the book is divided into three general categories. The first category includes papers on non-classical logics, including intuitionistic logic, constructive logic, basic logic, and substructural logic. The second category is made up of papers discussing issues in the contemporary philosophy of mathematics and logic. The third category contains papers on Avicenna’s logic and philosophy. Mohammad Ardeshir is a full professor of mathematical logic at the Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran, where he has taught generations of students for around a quarter century. Mohammad Ardeshir is known in the first place for his prominent works in basic logic and constructive mathematics. His areas of interest are however much broader and include topics in intuitionistic philosophy of mathematics and Arabic philosophy of logic and mathematics. In addition to numerous research articles in leading international journals, Ardeshir is the author of a highly praised Persian textbook in mathematical logic. Partly through his writings and translations, the school of mathematical intuitionism was introduced to the Iranian academic community.
Author : Henk Barendregt
Publisher : Cambridge University Press
Page : 969 pages
File Size : 37,22 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.
