Godels Theorems And Zermelos Axioms PDF Download
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Author | : Lorenz Halbeisen |
Publisher | : Springer Nature |
Total Pages | : 236 |
Release | : 2020-10-16 |
Genre | : Mathematics |
ISBN | : 3030522792 |
Download Gödel's Theorems and Zermelo's Axioms Book in PDF, ePub and Kindle
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.
Author | : Peter Smith |
Publisher | : Cambridge University Press |
Total Pages | : 376 |
Release | : 2007-07-26 |
Genre | : Mathematics |
ISBN | : 0521857848 |
Download An Introduction to Gödel's Theorems Book in PDF, ePub and Kindle
Peter Smith examines Gödel's Theorems, how they were established and why they matter.
Author | : Stuart Shanker |
Publisher | : Psychology Press |
Total Pages | : 272 |
Release | : 1989 |
Genre | : Gödel's theorem |
ISBN | : 0415045754 |
Download Gödel's Theorem in Focus Book in PDF, ePub and Kindle
A layman's guide to the mechanics of Gödel's proof together with a lucid discussion of the issues which it raises. Includes an essay discussing the significance of Gödel's work in the light of Wittgenstein's criticisms.
Author | : Richard Zach |
Publisher | : Createspace Independent Publishing Platform |
Total Pages | : 228 |
Release | : 2017-06-15 |
Genre | : |
ISBN | : 9781548138080 |
Download Incompleteness and Computability Book in PDF, ePub and Kindle
A textbook on recursive function theory and G�del's incompleteness theorems. Also covers models of arithmetic and second-order logic.
Author | : Alfred North Whitehead |
Publisher | : |
Total Pages | : 696 |
Release | : 1910 |
Genre | : Logic, Symbolic and mathematical |
ISBN | : |
Download Principia Mathematica Book in PDF, ePub and Kindle
Author | : Raymond M. Smullyan |
Publisher | : Knopf |
Total Pages | : 286 |
Release | : 2012-07-04 |
Genre | : Mathematics |
ISBN | : 0307962466 |
Download Forever Undecided Book in PDF, ePub and Kindle
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 | : Lorenz J. Halbeisen |
Publisher | : Springer |
Total Pages | : 594 |
Release | : 2017-12-20 |
Genre | : Mathematics |
ISBN | : 3319602314 |
Download Combinatorial Set Theory Book in PDF, ePub and Kindle
This book, now in a thoroughly revised second edition, provides a comprehensive and accessible introduction to modern set theory. Following an overview of basic notions in combinatorics and first-order logic, the author outlines the main topics of classical set theory in the second part, including Ramsey theory and the axiom of choice. The revised edition contains new permutation models and recent results in set theory without the axiom of choice. The third part explains the sophisticated technique of forcing in great detail, now including a separate chapter on Suslin’s problem. The technique is used to show that certain statements are neither provable nor disprovable from the axioms of set theory. In the final part, some topics of classical set theory are revisited and further developed in light of forcing, with new chapters on Sacks Forcing and Shelah’s astonishing construction of a model with finitely many Ramsey ultrafilters. Written for graduate students in axiomatic set theory, Combinatorial Set Theory will appeal to all researchers interested in the foundations of mathematics. With extensive reference lists and historical remarks at the end of each chapter, this book is suitable for self-study.
Author | : Kurt Gödel |
Publisher | : Courier Corporation |
Total Pages | : 82 |
Release | : 2012-05-24 |
Genre | : Mathematics |
ISBN | : 0486158403 |
Download On Formally Undecidable Propositions of Principia Mathematica and Related Systems Book in PDF, ePub and Kindle
First English translation of revolutionary paper (1931) that established that even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. Introduction by R. B. Braithwaite.
Author | : Raymond M. Smullyan |
Publisher | : Oxford University Press |
Total Pages | : 156 |
Release | : 1992-08-20 |
Genre | : Mathematics |
ISBN | : 0195364376 |
Download Godel's Incompleteness Theorems Book in PDF, ePub and Kindle
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.
Author | : D. Hilbert |
Publisher | : American Mathematical Society |
Total Pages | : 187 |
Release | : 2022-05-11 |
Genre | : Mathematics |
ISBN | : 147047056X |
Download Principles of Mathematical Logic Book in PDF, ePub and Kindle
David Hilbert was particularly interested in the foundations of mathematics. Among many other things, he is famous for his attempt to axiomatize mathematics. This now classic text is his treatment of symbolic logic. This translation is based on the second German edition and has been modified according to the criticisms of Church and Quine. In particular, the authors' original formulation of Gödel's completeness proof for the predicate calculus has been updated. In the first half of the twentieth century, an important debate on the foundations of mathematics took place. Principles of Mathematical Logic represents one of Hilbert's important contributions to that debate. Although symbolic logic has grown considerably in the subsequent decades, this book remains a classic.