Introduction To Mathematical Logic Fourth Edition PDF Download
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Author | : Elliot Mendelsohn |
Publisher | : Springer Science & Business Media |
Total Pages | : 351 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 1461572886 |
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This is a compact mtroduction to some of the pnncipal tOpICS of mathematical logic . In the belief that beginners should be exposed to the most natural and easiest proofs, I have used free-swinging set-theoretic methods. The significance of a demand for constructive proofs can be evaluated only after a certain amount of experience with mathematical logic has been obtained. If we are to be expelled from "Cantor's paradise" (as nonconstructive set theory was called by Hilbert), at least we should know what we are missing. The major changes in this new edition are the following. (1) In Chapter 5, Effective Computability, Turing-computabIlity IS now the central notion, and diagrams (flow-charts) are used to construct Turing machines. There are also treatments of Markov algorithms, Herbrand-Godel-computability, register machines, and random access machines. Recursion theory is gone into a little more deeply, including the s-m-n theorem, the recursion theorem, and Rice's Theorem. (2) The proofs of the Incompleteness Theorems are now based upon the Diagonalization Lemma. Lob's Theorem and its connection with Godel's Second Theorem are also studied. (3) In Chapter 2, Quantification Theory, Henkin's proof of the completeness theorem has been postponed until the reader has gained more experience in proof techniques. The exposition of the proof itself has been improved by breaking it down into smaller pieces and using the notion of a scapegoat theory. There is also an entirely new section on semantic trees.
Author | : Elliott Mendelson |
Publisher | : CRC Press |
Total Pages | : 464 |
Release | : 1997-06-01 |
Genre | : Mathematics |
ISBN | : 9780412808302 |
Download Introduction to Mathematical Logic, Fourth Edition Book in PDF, ePub and Kindle
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.
Author | : Elliott Mendelson |
Publisher | : Van Nostrand Reinhold Company |
Total Pages | : 344 |
Release | : 1979 |
Genre | : Mathematics |
ISBN | : |
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Author | : Alfred Tarski |
Publisher | : Courier Corporation |
Total Pages | : 272 |
Release | : 2013-07-04 |
Genre | : Mathematics |
ISBN | : 0486318893 |
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This classic undergraduate treatment examines the deductive method in its first part and explores applications of logic and methodology in constructing mathematical theories in its second part. Exercises appear throughout.
Author | : Christopher C. Leary |
Publisher | : Lulu.com |
Total Pages | : 382 |
Release | : 2015 |
Genre | : Education |
ISBN | : 1942341075 |
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At the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this expansion of Leary's user-friendly 1st edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study. Updating the 1st Edition's treatment of languages, structures, and deductions, leading to rigorous proofs of Gödel's First and Second Incompleteness Theorems, the expanded 2nd Edition includes a new introduction to incompleteness through computability as well as solutions to selected exercises.
Author | : H.-D. Ebbinghaus |
Publisher | : Springer Science & Business Media |
Total Pages | : 290 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 1475723555 |
Download Mathematical Logic Book in PDF, ePub and Kindle
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.
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 | : Dirk van Dalen |
Publisher | : Springer Science & Business Media |
Total Pages | : 218 |
Release | : 2013-11-11 |
Genre | : Mathematics |
ISBN | : 3662023822 |
Download Logic and Structure Book in PDF, ePub and Kindle
New corrected printing of a well-established text on logic at the introductory level.
Author | : George S. Boolos |
Publisher | : Cambridge University Press |
Total Pages | : 365 |
Release | : 2007-09-17 |
Genre | : Computers |
ISBN | : 0521877520 |
Download Computability and Logic Book in PDF, ePub and Kindle
This fifth edition of 'Computability and Logic' covers not just the staple topics of an intermediate logic course such as Godel's incompleteness theorems, but also optional topics that include Turing's theory of computability and Ramsey's theorem.
Author | : Patrick Suppes |
Publisher | : Courier Corporation |
Total Pages | : 336 |
Release | : 2012-07-12 |
Genre | : Mathematics |
ISBN | : 0486138054 |
Download Introduction to Logic Book in PDF, ePub and Kindle
Part I of this coherent, well-organized text deals with formal principles of inference and definition. Part II explores elementary intuitive set theory, with separate chapters on sets, relations, and functions. Ideal for undergraduates.