Incompleteness And Computability

Author : Richard Zach
Publisher : Createspace Independent Publishing Platform
ISBN 13 : 9781548138080
Total Pages : 228 pages
Book Rating : 4.88/5 ( download)

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Download or read book Incompleteness and Computability written by Richard Zach and published by Createspace Independent Publishing Platform. This book was released on 2017-06-15 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: A textbook on recursive function theory and G�del's incompleteness theorems. Also covers models of arithmetic and second-order logic.

Author : Richard Zach
Publisher :
ISBN 13 : 9781077323391
Total Pages : 281 pages
Book Rating : 4.95/5 ( download)

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Download or read book Incompleteness and Computability written by Richard Zach and published by . This book was released on 2019-11-09 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to metamathematics and Gödel's theorems. It covers recursive function theory, arithmetization of syntax, the first and second incompleteness theorem, models of arithmetic, second-order logic, and the lambda calculus. It is based on the Open Logic Project, and available for free download at ic.openlogicproject.org.

Author : Peter Smith
Publisher : Cambridge University Press
ISBN 13 : 0521857848
Total Pages : 376 pages
Book Rating : 4.40/5 ( download)

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Download or read book An Introduction to Gödel's Theorems written by Peter Smith and published by Cambridge University Press. This book was released on 2007-07-26 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Peter Smith examines Gödel's Theorems, how they were established and why they matter.

Author : George S. Boolos
Publisher : Cambridge University Press
ISBN 13 : 0521877520
Total Pages : 365 pages
Book Rating : 4.27/5 ( download)

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Download or read book Computability and Logic written by George S. Boolos and published by Cambridge University Press. This book was released on 2007-09-17 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Raymond M. Smullyan
Publisher : Knopf
ISBN 13 : 0307962466
Total Pages : 286 pages
Book Rating : 4.61/5 ( download)

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Download or read book Forever Undecided written by Raymond M. Smullyan and published by Knopf. This book was released on 2012-07-04 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Forever Undecided is the most challenging yet of Raymond Smullyan’s puzzle collections. It is, at the same time, an introduction—ingenious, instructive, entertaining—to Gödel’s famous theorems. With all the wit and charm that have delighted readers of his previous books, Smullyan transports us once again to that magical island where knights always tell the truth and knaves always lie. Here we meet a new and amazing array of characters, visitors to the island, seeking to determine the natives’ identities. Among them: the census-taker McGregor; a philosophical-logician in search of his flighty bird-wife, Oona; and a regiment of Reasoners (timid ones, normal ones, conceited, modest, and peculiar ones) armed with the rules of propositional logic (if X is true, then so is Y). By following the Reasoners through brain-tingling exercises and adventures—including journeys into the “other possible worlds” of Kripke semantics—even the most illogical of us come to understand Gödel’s two great theorems on incompleteness and undecidability, some of their philosophical and mathematical implications, and why we, like Gödel himself, must remain Forever Undecided!

Author : George Boolos
Publisher : Harvard University Press
ISBN 13 : 9780674537675
Total Pages : 458 pages
Book Rating : 4.7X/5 ( download)

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Download or read book Logic, Logic, and Logic written by George Boolos and published by Harvard University Press. This book was released on 1998 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: George Boolos was one of the most prominent and influential logician-philosophers of recent times. This collection, nearly all chosen by Boolos himself shortly before his death, includes thirty papers on set theory, second-order logic, and plural quantifiers; on Frege, Dedekind, Cantor, and Russell; and on miscellaneous topics in logic and proof theory, including three papers on various aspects of the Gödel theorems. Boolos is universally recognized as the leader in the renewed interest in studies of Frege's work on logic and the philosophy of mathematics. John Burgess has provided introductions to each of the three parts of the volume, and also an afterword on Boolos's technical work in provability logic, which is beyond the scope of this volume.

Author : Neil D. Jones
Publisher : MIT Press
ISBN 13 : 9780262100649
Total Pages : 494 pages
Book Rating : 4.49/5 ( download)

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Download or read book Computability and Complexity written by Neil D. Jones and published by MIT Press. This book was released on 1997 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computability and complexity theory should be of central concern to practitioners as well as theorists. Unfortunately, however, the field is known for its impenetrability. Neil Jones's goal as an educator and author is to build a bridge between computability and complexity theory and other areas of computer science, especially programming. In a shift away from the Turing machine- and G�del number-oriented classical approaches, Jones uses concepts familiar from programming languages to make computability and complexity more accessible to computer scientists and more applicable to practical programming problems. According to Jones, the fields of computability and complexity theory, as well as programming languages and semantics, have a great deal to offer each other. Computability and complexity theory have a breadth, depth, and generality not often seen in programming languages. The programming language community, meanwhile, has a firm grasp of algorithm design, presentation, and implementation. In addition, programming languages sometimes provide computational models that are more realistic in certain crucial aspects than traditional models. New results in the book include a proof that constant time factors do matter for its programming-oriented model of computation. (In contrast, Turing machines have a counterintuitive "constant speedup" property: that almost any program can be made to run faster, by any amount. Its proof involves techniques irrelevant to practice.) Further results include simple characterizations in programming terms of the central complexity classes PTIME and LOGSPACE, and a new approach to complete problems for NLOGSPACE, PTIME, NPTIME, and PSPACE, uniformly based on Boolean programs. Foundations of Computing series

Author : A. Sernadas
Publisher :
ISBN 13 : 9781904987888
Total Pages : 0 pages
Book Rating : 4.85/5 ( download)

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Download or read book Foundations of Logic and Theory of Computation written by A. Sernadas and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a self-contained introduction to mathematical logic and computability theory for students of mathematics or computer science. It is organized around the failures and successes of Hilbert's programme for the formalization of Mathematics. It is widely known that the programme failed with Gödel's incompleteness theorems and related negative results about arithmetic. Unfortunately, the positive outcomes of the programme are less well known, even among mathematicians. The book covers key successes, like Gödel's proof of the completeness of first-order logic, Gentzen's proof of its consistency by purely symbolic means, and the decidability of a couple of useful theories. The book also tries to convey the message that Hilbert's programme made a significant contribution to the advent of the computer as it is nowadays understood and, thus, to the latest industrial revolution. Part I of the book addresses Hilbert's programme and computability. Part II presents first-order logic, including Gödel's completeness theorem and Gentzen's consistency theorem. Part III is focused on arithmetic, representability of computable maps, Gödel's incompleteness theorems and decidability of Presburger arithmetic. Part IV provides detailed answers to selected exercises. The book can be used at late undergraduate level or early graduate level. An undergraduate course would concentrate on Parts I and II, leaving out the Gentzen calculus, and sketching the way to the 1st incompleteness theorem. A more advanced course might skip early material already known to the students and concentrate on the positive and negative results of Hilbert's programme, thus covering Gentzen's proof of consistency and Part III in full.

Author : B. Jack Copeland
Publisher : MIT Press
ISBN 13 : 0262527480
Total Pages : 373 pages
Book Rating : 4.84/5 ( download)

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Download or read book Computability written by B. Jack Copeland and published by MIT Press. This book was released on 2015-01-30 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer scientists, mathematicians, and philosophers discuss the conceptual foundations of the notion of computability as well as recent theoretical developments. In the 1930s a series of seminal works published by Alan Turing, Kurt Gödel, Alonzo Church, and others established the theoretical basis for computability. This work, advancing precise characterizations of effective, algorithmic computability, was the culmination of intensive investigations into the foundations of mathematics. In the decades since, the theory of computability has moved to the center of discussions in philosophy, computer science, and cognitive science. In this volume, distinguished computer scientists, mathematicians, logicians, and philosophers consider the conceptual foundations of computability in light of our modern understanding. Some chapters focus on the pioneering work by Turing, Gödel, and Church, including the Church-Turing thesis and Gödel's response to Church's and Turing's proposals. Other chapters cover more recent technical developments, including computability over the reals, Gödel's influence on mathematical logic and on recursion theory and the impact of work by Turing and Emil Post on our theoretical understanding of online and interactive computing; and others relate computability and complexity to issues in the philosophy of mind, the philosophy of science, and the philosophy of mathematics. Contributors Scott Aaronson, Dorit Aharonov, B. Jack Copeland, Martin Davis, Solomon Feferman, Saul Kripke, Carl J. Posy, Hilary Putnam, Oron Shagrir, Stewart Shapiro, Wilfried Sieg, Robert I. Soare, Umesh V. Vazirani

Author : Dexter C. Kozen
Publisher : Springer
ISBN 13 : 364285706X
Total Pages : 399 pages
Book Rating : 4.65/5 ( download)

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Download or read book Automata and Computability written by Dexter C. Kozen and published by Springer. This book was released on 2013-11-11 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: These are my lecture notes from CS381/481: Automata and Computability Theory, a one-semester senior-level course I have taught at Cornell Uni versity for many years. I took this course myself in thc fall of 1974 as a first-year Ph.D. student at Cornell from Juris Hartmanis and have been in love with the subject ever sin,:e. The course is required for computer science majors at Cornell. It exists in two forms: CS481, an honors version; and CS381, a somewhat gentler paced version. The syllabus is roughly the same, but CS481 go es deeper into thc subject, covers more material, and is taught at a more abstract level. Students are encouraged to start off in one or the other, then switch within the first few weeks if they find the other version more suitaLle to their level of mathematical skill. The purpose of t.hc course is twofold: to introduce computer science students to the rieh heritage of models and abstractions that have arisen over the years; and to dew!c'p the capacity to form abstractions of their own and reason in terms of them.