Mathematical Logic And Formal Systems
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Mathematical Logic and Formal Systems
This unique collection of research papers provides an important contribution to the area of Mathematical Logic and Formal Systems. Exploring interesting practical applications as well as problems for further investigation, this single-source reference discusses the interpretations of the concept of probability and their relationship to statistical methods ... illustrates the problem of set theoretical foundations and category theory ... treats the various aspects of the theory of large cardinals including combinatorial properties of some sets naturally related to them ... resolves an open problem in the theory of relations ... and characterizes interpretations of elementary theories as functors between categories whose objects are structures. Written by world-renowned authorities in their fields, Mathematical Logic and Formal Systems is important reading for logicians, pure and applied mathematicians, and graduate students in logic courses. Book jacket.
Mathematical Logic
Author: Wei Li
language: en
Publisher: Springer Science & Business Media
Release Date: 2010-02-26
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.
The Mathematics of Logic
Author: Richard W. Kaye
language: en
Publisher: Cambridge University Press
Release Date: 2007-07-12
This undergraduate textbook covers the key material for a typical first course in logic, in particular presenting a full mathematical account of the most important result in logic, the Completeness Theorem for first-order logic. Looking at a series of interesting systems, increasing in complexity, then proving and discussing the Completeness Theorem for each, the author ensures that the number of new concepts to be absorbed at each stage is manageable, whilst providing lively mathematical applications throughout. Unfamiliar terminology is kept to a minimum, no background in formal set-theory is required, and the book contains proofs of all the required set theoretical results. The reader is taken on a journey starting with König's Lemma, and progressing via order relations, Zorn's Lemma, Boolean algebras, and propositional logic, to completeness and compactness of first-order logic. As applications of the work on first-order logic, two final chapters provide introductions to model theory and nonstandard analysis.