Introduction To Incompleteness
DOWNLOAD
Download Introduction To Incompleteness PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Introduction To Incompleteness book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Introduction To Incompleteness
DOWNLOAD
Author : Serafim Batzoglou
language : en
Publisher: Springer Nature
Release Date : 2024-08-30
Introduction To Incompleteness written by Serafim Batzoglou and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-30 with Mathematics categories.
Incompleteness is a fascinating phenomenon at the intersection of mathematical foundations, computer science, and epistemology that places a limit on what is provable. However, despite its importance, it is often overlooked in the mathematics curricula because it is difficult to teach. This book aims to help bridge this pedagogical gap by providing a complete and accessible technical exposition of incompleteness for a wide audience. The author accomplishes this by making conceptually difficult proofs more approachable by providing intuitive explanations of the main ideas. Care is taken to emphasize the different layers of the mathematical argument – the layer within and the metalayer about an axiomatic system. Structurally, the book efficiently examines key results and arrives at some of the most interesting concepts as quickly as possible. It begins with Gödel's incompleteness theorems before continuing on to challenging concepts in the arithmetized completeness theorem, the Paris-Harrington theorem, and the independence of the continuum hypothesis. Other topics covered include the Lucas-Penrose arguments, ordinals and cardinals, and axiomatic set theory. Additionally, the author’s coverage of forcing is a notable addition to the existing literature. Introduction to Incompleteness will be of interest to researchers, students, and instructors looking for a resource to teach this topic. It may also be suitable for self-study. Knowledge of undergraduate-level theoretical mathematics or computer science is required, as well as a familiarity with abstract proofs.
Incompleteness And Computability
DOWNLOAD
Author : Richard Zach
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2017-06-15
Incompleteness And Computability written by Richard Zach and has been published by Createspace Independent Publishing Platform this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-15 with categories.
A textbook on recursive function theory and G�del's incompleteness theorems. Also covers models of arithmetic and second-order logic.
Incompleteness
DOWNLOAD
Author : Rebecca Goldstein
language : en
Publisher: W. W. Norton & Company
Release Date : 2006-01-31
Incompleteness written by Rebecca Goldstein and has been published by W. W. Norton & Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-31 with Biography & Autobiography categories.
"An introduction to the life and thought of Kurt Gödel, who transformed our conception of math forever"--Provided by publisher.
Godel S Incompleteness Theorems
DOWNLOAD
Author : Raymond M. Smullyan
language : en
Publisher: Oxford University Press
Release Date : 1992-08-20
Godel S Incompleteness Theorems written by Raymond M. Smullyan and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-08-20 with Mathematics categories.
Kurt Godel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently "undecidable." His work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum theory brought him further worldwide fame. In this introductory volume, Raymond Smullyan, himself a well-known logician, guides the reader through the fascinating world of Godel's incompleteness theorems. The level of presentation is suitable for anyone with a basic acquaintance with mathematical logic. As a clear, concise introduction to a difficult but essential subject, the book will appeal to mathematicians, philosophers, and computer scientists.
G Del S Theorem
DOWNLOAD
Author : Torkel Franzén
language : en
Publisher: CRC Press
Release Date : 2005-06-06
G Del S Theorem written by Torkel Franzén and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-06 with Mathematics categories.
"Among the many expositions of Gödel's incompleteness theorems written for non-specialists, this book stands apart. With exceptional clarity, Franzén gives careful, non-technical explanations both of what those theorems say and, more importantly, what they do not. No other book aims, as his does, to address in detail the misunderstandings and abuses of the incompleteness theorems that are so rife in popular discussions of their significance. As an antidote to the many spurious appeals to incompleteness in theological, anti-mechanist and post-modernist debates, it is a valuable addition to the literature." --- John W. Dawson, author of Logical Dilemmas: The Life and Work of Kurt Gödel
The Incompleteness Phenomenon
DOWNLOAD
Author : Martin Goldstern
language : en
Publisher: CRC Press
Release Date : 2018-10-08
The Incompleteness Phenomenon written by Martin Goldstern and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-08 with Mathematics categories.
This introduction to mathematical logic takes Gödel's incompleteness theorem as a starting point. It goes beyond a standard text book and should interest everyone from mathematicians to philosophers and general readers who wish to understand the foundations and limitations of modern mathematics.
G Del S Theorems And Zermelo S Axioms
DOWNLOAD
Author : Lorenz Halbeisen
language : en
Publisher: Springer Nature
Release Date : 2020-10-16
G Del S Theorems And Zermelo S Axioms written by Lorenz Halbeisen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-16 with Mathematics categories.
This book provides a concise and self-contained introduction to the foundations of mathematics. The first part covers the fundamental notions of mathematical logic, including logical axioms, formal proofs and the basics of model theory. Building on this, in the second and third part of the book the authors present detailed proofs of Gödel’s classical completeness and incompleteness theorems. In particular, the book includes a full proof of Gödel’s second incompleteness theorem which states that it is impossible to prove the consistency of arithmetic within its axioms. The final part is dedicated to an introduction into modern axiomatic set theory based on the Zermelo’s axioms, containing a presentation of Gödel’s constructible universe of sets. A recurring theme in the whole book consists of standard and non-standard models of several theories, such as Peano arithmetic, Presburger arithmetic and the real numbers. The book addresses undergraduate mathematics students and is suitable for a one or two semester introductory course into logic and set theory. Each chapter concludes with a list of exercises.
Proofs And Algorithms
DOWNLOAD
Author : Gilles Dowek
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-11
Proofs And Algorithms written by Gilles Dowek and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-11 with Computers categories.
Logic is a branch of philosophy, mathematics and computer science. It studies the required methods to determine whether a statement is true, such as reasoning and computation. Proofs and Algorithms: Introduction to Logic and Computability is an introduction to the fundamental concepts of contemporary logic - those of a proof, a computable function, a model and a set. It presents a series of results, both positive and negative, - Church's undecidability theorem, Gödel’s incompleteness theorem, the theorem asserting the semi-decidability of provability - that have profoundly changed our vision of reasoning, computation, and finally truth itself. Designed for undergraduate students, this book presents all that philosophers, mathematicians and computer scientists should know about logic.
On Formally Undecidable Propositions Of Principia Mathematica And Related Systems
DOWNLOAD
Author : Kurt Gödel
language : en
Publisher: Courier Corporation
Release Date : 1992-01-01
On Formally Undecidable Propositions Of Principia Mathematica And Related Systems written by Kurt Gödel and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-01 with Mathematics categories.
In 1931, a young Austrian mathematician published an epoch-making paper containing one of the most revolutionary ideas in logic since Aristotle. Kurt Giidel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. The repercussions of this discovery are still being felt and debated in 20th-century mathematics. The present volume reprints the first English translation of Giidel's far-reaching work. Not only does it make the argument more intelligible, but the introduction contributed by Professor R. B. Braithwaite (Cambridge University}, an excellent work of scholarship in its own right, illuminates it by paraphrasing the major part of the argument. This Dover edition thus makes widely available a superb edition of a classic work of original thought, one that will be of profound interest to mathematicians, logicians and anyone interested in the history of attempts to establish axioms that would provide a rigorous basis for all mathematics. Translated by B. Meltzer, University of Edinburgh. Preface. Introduction by R. B. Braithwaite.
Inexhaustibility
DOWNLOAD
Author : Torkel Franzén
language : en
Publisher: Cambridge University Press
Release Date : 2017-03-30
Inexhaustibility written by Torkel Franzén and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-30 with Mathematics categories.
Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the sixteenth publication in the Lecture Notes in Logic series, gives a sustained presentation of a particular view of the topic of Gödelian extensions of theories. It presents the basic material in predicate logic, set theory and recursion theory, leading to a proof of Gödel's incompleteness theorems. The inexhaustibility of mathematics is treated based on the concept of transfinite progressions of theories as conceived by Turing and Feferman. All concepts and results are introduced as needed, making the presentation self-contained and thorough. Philosophers, mathematicians and others will find the book helpful in acquiring a basic grasp of the philosophical and logical results and issues.