a tour through mathematical logic

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A Tour Through Mathematical Logic

Author : Robert S. Wolf
ISBN : 0883850362
Genre : Mathematics
File Size : 61. 82 MB
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The foundations of mathematics include mathematical logic, set theory, recursion theory, model theory, and Gdel's incompleteness theorems. Professor Wolf provides here a guide that any interested reader with some post-calculus experience in mathematics can read, enjoy, and learn from. It could also serve as a textbook for courses in the foundations of mathematics, at the undergraduate or graduate level. The book is deliberately less structured and more user-friendly than standard texts on foundations, so will also be attractive to those outside the classroom environment wanting to learn about the subject.

A Tour Through Mathematical Logic

Author : Robert S. Wolf
ISBN : 0883850362
Genre : Mathematics
File Size : 44. 62 MB
Format : PDF, ePub, Docs
Download : 978
Read : 807

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The foundations of mathematics include mathematical logic, set theory, recursion theory, model theory, and Gdel's incompleteness theorems. Professor Wolf provides here a guide that any interested reader with some post-calculus experience in mathematics can read, enjoy, and learn from. It could also serve as a textbook for courses in the foundations of mathematics, at the undergraduate or graduate level. The book is deliberately less structured and more user-friendly than standard texts on foundations, so will also be attractive to those outside the classroom environment wanting to learn about the subject.

Mathematical Logic

Author : George Tourlakis
ISBN : 9781118030691
Genre : Mathematics
File Size : 43. 23 MB
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A comprehensive and user-friendly guide to the use of logic inmathematical reasoning Mathematical Logic presents a comprehensive introductionto formal methods of logic and their use as a reliable tool fordeductive reasoning. With its user-friendly approach, this booksuccessfully equips readers with the key concepts and methods forformulating valid mathematical arguments that can be used touncover truths across diverse areas of study such as mathematics,computer science, and philosophy. The book develops the logical tools for writing proofs byguiding readers through both the established "Hilbert" style ofproof writing, as well as the "equational" style that is emergingin computer science and engineering applications. Chapters havebeen organized into the two topical areas of Boolean logic andpredicate logic. Techniques situated outside formal logic areapplied to illustrate and demonstrate significant facts regardingthe power and limitations of logic, such as: Logic can certify truths and only truths. Logic can certify all absolute truths (completeness theorems ofPost and Gödel). Logic cannot certify all "conditional" truths, such as thosethat are specific to the Peano arithmetic. Therefore, logic hassome serious limitations, as shown through Gödel'sincompleteness theorem. Numerous examples and problem sets are provided throughout thetext, further facilitating readers' understanding of thecapabilities of logic to discover mathematical truths. In addition,an extensive appendix introduces Tarski semantics and proceeds withdetailed proofs of completeness and first incompleteness theorems,while also providing a self-contained introduction to the theory ofcomputability. With its thorough scope of coverage and accessible style,Mathematical Logic is an ideal book for courses inmathematics, computer science, and philosophy at theupper-undergraduate and graduate levels. It is also a valuablereference for researchers and practitioners who wish to learn howto use logic in their everyday work.

An Introduction To Mathematical Logic And Type Theory

Author : Peter B. Andrews
ISBN : 9789401599344
Genre : Mathematics
File Size : 40. 69 MB
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In case you are considering to adopt this book for courses with over 50 students, please contact ties.nijssen@springer.com 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.

A Concise Introduction To Mathematical Logic

Author : Wolfgang Rautenberg
ISBN : 1441912215
Genre : Mathematics
File Size : 68. 68 MB
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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.

Handbook Of Mathematical Logic

Author : J. Barwise
ISBN : 0080933645
Genre : Mathematics
File Size : 79. 52 MB
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The handbook is divided into four parts: model theory, set theory, recursion theory and proof theory. Each of the four parts begins with a short guide to the chapters that follow. Each chapter is written for non-specialists in the field in question. Mathematicians will find that this book provides them with a unique opportunity to apprise themselves of developments in areas other than their own.

A Profile Of Mathematical Logic

Author : Howard DeLong
ISBN : 9780486139159
Genre : Mathematics
File Size : 73. 49 MB
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This introduction to mathematical logic explores philosophical issues and Gödel's Theorem. Its widespread influence extends to the author of Gödel, Escher, Bach, whose Pulitzer Prize–winning book was inspired by this work.

Proof Logic And Conjecture

Author : Robert S. Wolf
ISBN : 0716730502
Genre : Mathematics
File Size : 46. 12 MB
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This text is designed to teach students how to read and write proofs in mathematics and to acquaint them with how mathematicians investigate problems and formulate conjecture.

Introduction To Mathematical Logic Fourth Edition

Author : Elliott Mendelson
ISBN : 0412808307
Genre : Mathematics
File Size : 58. 28 MB
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The Fourth Edition of this long-established text retains all the key features of the previous editions, covering the basic topics of a solid first course in mathematical logic. This edition includes an extensive appendix on second-order logic, a section on set theory with urlements, and a section on the logic that results when we allow models with empty domains. The text contains numerous exercises and an appendix furnishes answers to many of them. Introduction to Mathematical Logic includes: propositional logic first-order logic first-order number theory and the incompleteness and undecidability theorems of Gödel, Rosser, Church, and Tarski axiomatic set theory theory of computability The study of mathematical logic, axiomatic set theory, and computability theory provides an understanding of the fundamental assumptions and proof techniques that form basis of mathematics. Logic and computability theory have also become indispensable tools in theoretical computer science, including artificial intelligence. Introduction to Mathematical Logic covers these topics in a clear, reader-friendly style that will be valued by anyone working in computer science as well as lecturers and researchers in mathematics, philosophy, and related fields.

Mathematical Logic

Author : H.-D. Ebbinghaus
ISBN : 9781475723557
Genre : Mathematics
File Size : 22. 56 MB
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This introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines. It covers several advanced topics not commonly treated in introductory texts, such as Fraïssé's characterization of elementary equivalence, Lindström's theorem on the maximality of first-order logic, and the fundamentals of logic programming.

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