Author : Paul C. Rosenbloom
Publisher :
Page : 234 pages
File Size : 50,67 MB
Release : 1950
Category : Logic, Symbolic and mathematical
ISBN :
"This book is intended for readers who, while mature mathematically, have no knowledge of mathematical logic. We attempt to introduce the reader to the most important approaches to the subject, and, wherever possible within the limitations of space which we have set for ourselves, to give at least a few nontrivial results illustrating each of the important methods for attacking logical problems"--Preface.
Author : Georg Kreisel
Publisher : Elsevier
Page : 222 pages
File Size : 38,82 MB
Release : 1967
Category : Electronic books
ISBN : 9780444534125
Author : Jerzy Słupecki
Publisher : Pergamon
Page : 374 pages
File Size : 30,94 MB
Release : 1967
Category : Mathematics
ISBN :
Author : Jan Łukasiewicz
Publisher :
Page : 127 pages
File Size : 40,48 MB
Release : 1966
Category : Logic, Symbolic and mathematical
ISBN :
Author : Jerzy Słupecki
Publisher : Pergamon
Page : 374 pages
File Size : 11,17 MB
Release : 1967
Category : Mathematics
ISBN :
Author : Roman Kossak
Publisher : Springer
Page : 188 pages
File Size : 20,46 MB
Release : 2018-10-03
Category : Mathematics
ISBN : 3319972987
This book, presented in two parts, offers a slow introduction to mathematical logic, and several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions. Its first part, Logic Sets, and Numbers, shows how mathematical logic is used to develop the number structures of classical mathematics. The exposition does not assume any prerequisites; it is rigorous, but as informal as possible. All necessary concepts are introduced exactly as they would be in a course in mathematical logic; but are accompanied by more extensive introductory remarks and examples to motivate formal developments. The second part, Relations, Structures, Geometry, introduces several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions, and shows how they are used to study and classify mathematical structures. Although more advanced, this second part is accessible to the reader who is either already familiar with basic mathematical logic, or has carefully read the first part of the book. Classical developments in model theory, including the Compactness Theorem and its uses, are discussed. Other topics include tameness, minimality, and order minimality of structures. The book can be used as an introduction to model theory, but unlike standard texts, it does not require familiarity with abstract algebra. This book will also be of interest to mathematicians who know the technical aspects of the subject, but are not familiar with its history and philosophical background.
Author : Wolfgang Rautenberg
Publisher : Springer
Page : 337 pages
File Size : 33,89 MB
Release : 2010-07-01
Category : Mathematics
ISBN : 1441912215
Mathematical logic developed into a broad discipline with many applications in mathematics, informatics, linguistics and philosophy. This text introduces the fundamentals of this field, and this new edition has been thoroughly expanded and revised.
Author : D.L. Johnson
Publisher : Springer Science & Business Media
Page : 179 pages
File Size : 19,15 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1447106032
In mathematics we are interested in why a particular formula is true. Intuition and statistical evidence are insufficient, so we need to construct a formal logical proof. The purpose of this book is to describe why such proofs are important, what they are made of, how to recognize valid ones, how to distinguish different kinds, and how to construct them. This book is written for 1st year students with no previous experience of formulating proofs. Dave Johnson has drawn from his considerable experience to provide a text that concentrates on the most important elements of the subject using clear, simple explanations that require no background knowledge of logic. It gives many useful examples and problems, many with fully-worked solutions at the end of the book. In addition to a comprehensive index, there is also a useful `Dramatis Personae` an index to the many symbols introduced in the text, most of which will be new to students and which will be used throughout their degree programme.
Author : Wei Li
Publisher : Springer Science & Business Media
Page : 273 pages
File Size : 43,13 MB
Release : 2010-02-26
Category : Mathematics
ISBN : 3764399775
Mathematical logic is a branch of mathematics that takes axiom systems and mathematical proofs as its objects of study. This book shows how it can also provide a foundation for the development of information science and technology. The first five chapters systematically present the core topics of classical mathematical logic, including the syntax and models of first-order languages, formal inference systems, computability and representability, and Gödel’s theorems. The last five chapters present extensions and developments of classical mathematical logic, particularly the concepts of version sequences of formal theories and their limits, the system of revision calculus, proschemes (formal descriptions of proof methods and strategies) and their properties, and the theory of inductive inference. All of these themes contribute to a formal theory of axiomatization and its application to the process of developing information technology and scientific theories. The book also describes the paradigm of three kinds of language environments for theories and it presents the basic properties required of a meta-language environment. Finally, the book brings these themes together by describing a workflow for scientific research in the information era in which formal methods, interactive software and human invention are all used to their advantage. This book represents a valuable reference for graduate and undergraduate students and researchers in mathematics, information science and technology, and other relevant areas of natural sciences. Its first five chapters serve as an undergraduate text in mathematical logic and the last five chapters are addressed to graduate students in relevant disciplines.
Author : Jan Lukasiewicz
Publisher :
Page : 127 pages
File Size : 31,62 MB
Release : 1991
Category :
ISBN :
