Mathematical Logic And Formalized Theories PDF Download
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| Author | : Robert L. Rogers |
| Publisher | : Elsevier |
| Total Pages | : 248 |
| Release | : 2014-05-12 |
| Genre | : Mathematics |
| ISBN | : 1483257975 |
Download Mathematical Logic and Formalized Theories Book in PDF, ePub and Kindle
Mathematical Logic and Formalized Theories: A Survey of Basic Concepts and Results focuses on basic concepts and results of mathematical logic and the study of formalized theories. The manuscript first elaborates on sentential logic and first-order predicate logic. Discussions focus on first-order predicate logic with identity and operation symbols, first-order predicate logic with identity, completeness theorems, elementary theories, deduction theorem, interpretations, truth, and validity, sentential connectives, and tautologies. The text then tackles second-order predicate logic, as well as second-order theories, theory of definition, and second-order predicate logic F2. The publication takes a look at natural and real numbers, incompleteness, and the axiomatic set theory. Topics include paradoxes, recursive functions and relations, Gödel's first incompleteness theorem, axiom of choice, metamathematics of R and elementary algebra, and metamathematics of N. The book is a valuable reference for mathematicians and researchers interested in mathematical logic and formalized theories.
| Author | : Robert Rogers |
| Publisher | : |
| Total Pages | : |
| Release | : 1974 |
| Genre | : |
| ISBN | : |
Download Mathematical Logic and Formalized Theories Book in PDF, ePub and Kindle
| Author | : Richard E. Hodel |
| Publisher | : Courier Corporation |
| Total Pages | : 514 |
| Release | : 2013-01-01 |
| Genre | : Mathematics |
| ISBN | : 0486497852 |
Download An Introduction to Mathematical Logic Book in PDF, ePub and Kindle
This comprehensive overview ofmathematical logic is designedprimarily for advanced undergraduatesand graduate studentsof mathematics. The treatmentalso contains much of interest toadvanced students in computerscience and philosophy. Topics include propositional logic;first-order languages and logic; incompleteness, undecidability,and indefinability; recursive functions; computability;and Hilbert’s Tenth Problem.Reprint of the PWS Publishing Company, Boston, 1995edition.
| Author | : Peter B. Andrews |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 404 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 9401599343 |
Download An Introduction to Mathematical Logic and Type Theory Book in PDF, ePub and Kindle
In case you are considering to adopt this book for courses with over 50 students, please contact [email protected] for more information. This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification.
| Author | : Alexander Prestel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 198 |
| Release | : 2011-08-21 |
| Genre | : Mathematics |
| ISBN | : 1447121767 |
Download Mathematical Logic and Model Theory Book in PDF, ePub and Kindle
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 | : Wei Li |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 273 |
| Release | : 2010-02-26 |
| Genre | : Mathematics |
| ISBN | : 3764399775 |
Download Mathematical Logic Book in PDF, ePub and Kindle
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 | : Catarina Dutilh Novaes |
| Publisher | : Cambridge University Press |
| Total Pages | : 285 |
| Release | : 2012-11-08 |
| Genre | : Computers |
| ISBN | : 1107020913 |
Download Formal Languages in Logic Book in PDF, ePub and Kindle
Examines the cognitive impact on formal languages for human reasoning, drawing on philosophy, historical development, psychology and cognitive science.
| Author | : Michael Detlefsen |
| Publisher | : Routledge |
| Total Pages | : 251 |
| Release | : 2005-07-08 |
| Genre | : Mathematics |
| ISBN | : 1134975287 |
Download Proof, Logic and Formalization Book in PDF, ePub and Kindle
A collection of essays from distinguished contributors looking at why it is that mathematical proof is given precedence over other forms of mathematical justification.
| Author | : Wolfgang Rautenberg |
| Publisher | : Springer |
| Total Pages | : 337 |
| Release | : 2010-07-01 |
| Genre | : Mathematics |
| ISBN | : 1441912215 |
Download A Concise Introduction to Mathematical Logic Book in PDF, ePub and Kindle
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 | : Paul C. Rosenbloom |
| Publisher | : |
| Total Pages | : 234 |
| Release | : 1950 |
| Genre | : Logic, Symbolic and mathematical |
| ISBN | : |
Download The Elements of Mathematical Logic Book in PDF, ePub and Kindle
"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.
